
==== Front
Eur Phys J C Part Fields
Eur Phys J C Part Fields
The European Physical Journal. C, Particles and Fields
1434-6044
1434-6052
Springer Berlin Heidelberg Berlin/Heidelberg

12258
10.1140/epjc/s10052-023-12258-4
Regular Article - Experimental Physics
Measurement of the production cross section for a W boson in association with a charm quark in proton–proton collisions at s=13TeV
CMS Collaborationhttp://orcid.org/0009-0000-0684-6742
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cms-publication-committee-chair@cern.ch

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1 https://ror.org/00ad27c73 grid.48507.3e 0000 0004 0482 7128 Yerevan Physics Institute, Yerevan, Armenia
2 https://ror.org/039shy520 grid.450258.e 0000 0004 0625 7405 Institut für Hochenergiephysik, Vienna, Austria
3 https://ror.org/008x57b05 grid.5284.b 0000 0001 0790 3681 Universiteit Antwerpen, Antwerpen, Belgium
4 https://ror.org/006e5kg04 grid.8767.e 0000 0001 2290 8069 Vrije Universiteit Brussel, Brussel, Belgium
5 https://ror.org/01r9htc13 grid.4989.c 0000 0001 2348 6355 Université Libre de Bruxelles, Bruxelles, Belgium
6 https://ror.org/00cv9y106 grid.5342.0 0000 0001 2069 7798 Ghent University, Ghent, Belgium
7 https://ror.org/02495e989 grid.7942.8 0000 0001 2294 713X Université Catholique de Louvain, Louvain-la-Neuve, Belgium
8 https://ror.org/02wnmk332 grid.418228.5 0000 0004 0643 8134 Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil
9 https://ror.org/0198v2949 grid.412211.5 0000 0004 4687 5267 Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil
10 grid.412368.a 0000 0004 0643 8839 Universidade Estadual Paulista, Universidade Federal do ABC, São Paulo, Brazil
11 grid.410344.6 0000 0001 2097 3094 Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria
12 https://ror.org/02jv3k292 grid.11355.33 0000 0001 2192 3275 University of Sofia, Sofia, Bulgaria
13 https://ror.org/04xe01d27 grid.412182.c 0000 0001 2179 0636 Instituto De Alta Investigación, Universidad de Tarapacá, Casilla 7 D, Arica, Chile
14 https://ror.org/00wk2mp56 grid.64939.31 0000 0000 9999 1211 Beihang University, Beijing, China
15 https://ror.org/03cve4549 grid.12527.33 0000 0001 0662 3178 Department of Physics, Tsinghua University, Beijing, China
16 https://ror.org/03v8tnc06 grid.418741.f 0000 0004 0632 3097 Institute of High Energy Physics, Beijing, China
17 https://ror.org/02v51f717 grid.11135.37 0000 0001 2256 9319 State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing, China
18 https://ror.org/0064kty71 grid.12981.33 0000 0001 2360 039X Sun Yat-Sen University, Guangzhou, China
19 https://ror.org/04c4dkn09 grid.59053.3a 0000 0001 2167 9639 University of Science and Technology of China, Hefei, China
20 grid.8547.e 0000 0001 0125 2443 Institute of Modern Physics and Key Laboratory of Nuclear Physics and Ion-beam Application (MOE), Fudan University, Shanghai, China
21 https://ror.org/00a2xv884 grid.13402.34 0000 0004 1759 700X Zhejiang University, Hangzhou, Zhejiang, China
22 https://ror.org/02mhbdp94 grid.7247.6 0000 0004 1937 0714 Universidad de Los Andes, Bogota, Colombia
23 https://ror.org/03bp5hc83 grid.412881.6 0000 0000 8882 5269 Universidad de Antioquia, Medellin, Colombia
24 https://ror.org/00m31ft63 grid.38603.3e 0000 0004 0644 1675 Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University of Split, Split, Croatia
25 https://ror.org/00m31ft63 grid.38603.3e 0000 0004 0644 1675 Faculty of Science, University of Split, Split, Croatia
26 https://ror.org/02mw21745 grid.4905.8 0000 0004 0635 7705 Institute Rudjer Boskovic, Zagreb, Croatia
27 https://ror.org/02qjrjx09 grid.6603.3 0000 0001 2116 7908 University of Cyprus, Nicosia, Cyprus
28 https://ror.org/024d6js02 grid.4491.8 0000 0004 1937 116X Charles University, Prague, Czech Republic
29 https://ror.org/01gb99w41 grid.440857.a 0000 0004 0485 2489 Escuela Politecnica Nacional, Quito, Ecuador
30 https://ror.org/01r2c3v86 grid.412251.1 0000 0000 9008 4711 Universidad San Francisco de Quito, Quito, Ecuador
31 grid.423564.2 0000 0001 2165 2866 Academy of Scientific Research and Technology of the Arab Republic of Egypt, Egyptian Network of High Energy Physics, Cairo, Egypt
32 https://ror.org/023gzwx10 grid.411170.2 0000 0004 0412 4537 Center for High Energy Physics (CHEP-FU), Fayoum University, El-Fayoum, Egypt
33 https://ror.org/03eqd4a41 grid.177284.f 0000 0004 0410 6208 National Institute of Chemical Physics and Biophysics, Tallinn, Estonia
34 https://ror.org/040af2s02 grid.7737.4 0000 0004 0410 2071 Department of Physics, University of Helsinki, Helsinki, Finland
35 https://ror.org/01x2x1522 grid.470106.4 0000 0001 1106 2387 Helsinki Institute of Physics, Helsinki, Finland
36 https://ror.org/0208vgz68 grid.12332.31 0000 0001 0533 3048 Lappeenranta-Lahti University of Technology, Lappeenranta, Finland
37 https://ror.org/03xjwb503 grid.460789.4 0000 0004 4910 6535 IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France
38 grid.508893.f Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau, France
39 https://ror.org/00pg6eq24 grid.11843.3f 0000 0001 2157 9291 Université de Strasbourg, CNRS, IPHC UMR 7178, Strasbourg, France
40 https://ror.org/02avf8f85 Institut de Physique des 2 Infinis de Lyon (IP2I ), Villeurbanne, France
41 https://ror.org/00aamz256 grid.41405.34 0000 0001 0702 1187 Georgian Technical University, Tbilisi, Georgia
42 https://ror.org/04xfq0f34 grid.1957.a 0000 0001 0728 696X I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
43 https://ror.org/04xfq0f34 grid.1957.a 0000 0001 0728 696X III. Physikalisches Institut A, RWTH Aachen University, Aachen, Germany
44 https://ror.org/04xfq0f34 grid.1957.a 0000 0001 0728 696X III. Physikalisches Institut B, RWTH Aachen University, Aachen, Germany
45 https://ror.org/01js2sh04 grid.7683.a 0000 0004 0492 0453 Deutsches Elektronen-Synchrotron, Hamburg, Germany
46 https://ror.org/00g30e956 grid.9026.d 0000 0001 2287 2617 University of Hamburg, Hamburg, Germany
47 https://ror.org/04t3en479 grid.7892.4 0000 0001 0075 5874 Karlsruher Institut fuer Technologie, Karlsruhe, Germany
48 grid.6083.d 0000 0004 0635 6999 Institute of Nuclear and Particle Physics (INPP), NCSR Demokritos, Agia Paraskevi, Greece
49 https://ror.org/04gnjpq42 grid.5216.0 0000 0001 2155 0800 National and Kapodistrian University of Athens, Athens, Greece
50 grid.4241.3 0000 0001 2185 9808 National Technical University of Athens, Athens, Greece
51 https://ror.org/01qg3j183 grid.9594.1 0000 0001 2108 7481 University of Ioánnina, Ioannina, Greece
52 https://ror.org/01jsq2704 grid.5591.8 0000 0001 2294 6276 MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös Loránd University, Budapest, Hungary
53 https://ror.org/035dsb084 grid.419766.b 0000 0004 1759 8344 Wigner Research Centre for Physics, Budapest, Hungary
54 grid.418861.2 0000 0001 0674 7808 Institute of Nuclear Research ATOMKI, Debrecen, Hungary
55 https://ror.org/02xf66n48 grid.7122.6 0000 0001 1088 8582 Institute of Physics, University of Debrecen, Debrecen, Hungary
56 Karoly Robert Campus, MATE Institute of Technology, Gyongyos, Hungary
57 https://ror.org/04p2sbk06 grid.261674.0 0000 0001 2174 5640 Panjab University, Chandigarh, India
58 https://ror.org/04gzb2213 grid.8195.5 0000 0001 2109 4999 University of Delhi, Delhi, India
59 https://ror.org/0491yz035 grid.473481.d 0000 0001 0661 8707 Saha Institute of Nuclear Physics, HBNI, Kolkata, India
60 https://ror.org/03v0r5n49 grid.417969.4 0000 0001 2315 1926 Indian Institute of Technology Madras, Madras, India
61 https://ror.org/05w6wfp17 grid.418304.a 0000 0001 0674 4228 Bhabha Atomic Research Centre, Mumbai, India
62 https://ror.org/03ht1xw27 grid.22401.35 0000 0004 0502 9283 Tata Institute of Fundamental Research-A, Mumbai, India
63 https://ror.org/03ht1xw27 grid.22401.35 0000 0004 0502 9283 Tata Institute of Fundamental Research-B, Mumbai, India
64 https://ror.org/02r2k1c68 grid.419643.d 0000 0004 1764 227X National Institute of Science Education and Research, An OCC of Homi Bhabha National Institute, Bhubaneswar, Odisha India
65 https://ror.org/028qa3n13 grid.417959.7 0000 0004 1764 2413 Indian Institute of Science Education and Research (IISER), Pune, India
66 grid.411751.7 0000 0000 9908 3264 Isfahan University of Technology, Isfahan, Iran
67 https://ror.org/04xreqs31 grid.418744.a 0000 0000 8841 7951 Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
68 https://ror.org/05m7pjf47 grid.7886.1 0000 0001 0768 2743 University College Dublin, Dublin, Ireland
69 grid.4466.0 0000 0001 0578 5482 INFN Sezione di Bari, Università di Bari, Politecnico di Bari, Bari, Italy
70 grid.6292.f 0000 0004 1757 1758 INFN Sezione di Bologna, Università di Bologna, Bologna, Italy
71 grid.8158.4 0000 0004 1757 1969 INFN Sezione di Catania, Università di Catania, Catania, Italy
72 https://ror.org/02vv5y108 grid.470204.5 0000 0001 2231 4148 INFN Sezione di Firenze, Università di Firenze, Firenze, Italy
73 https://ror.org/049jf1a25 grid.463190.9 0000 0004 0648 0236 INFN Laboratori Nazionali di Frascati, Frascati, Italy
74 grid.5606.5 0000 0001 2151 3065 INFN Sezione di Genova, Università di Genova, Genoa, Italy
75 https://ror.org/03xejxm22 grid.470207.6 0000 0004 8390 4143 INFN Sezione di Milano-Bicocca, Università di Milano-Bicocca, Milan, Italy
76 https://ror.org/015kcdd40 grid.470211.1 0000 0004 8343 7696 INFN Sezione di Napoli, Università di Napoli ’Federico II’, Napoli, Italy; Università della Basilicata, Potenza, Italy, Università G. Marconi, Rome, Italy
77 grid.11696.39 0000 0004 1937 0351 INFN Sezione di Padova, Università di Padova, Padova, Italy; Università di Trento, Trento, Italy
78 grid.8982.b 0000 0004 1762 5736 INFN Sezione di Pavia, Università di Pavia, Pavia, Italy
79 grid.9027.c 0000 0004 1757 3630 INFN Sezione di Perugia, Università di Perugia, Perugia, Italy
80 grid.9024.f 0000 0004 1757 4641 INFN Sezione di Pisa, Università di Pisa, Scuola Normale Superiore di Pisa, Pisa, Italy; Università di Siena, Siena, Italy
81 grid.7841.a INFN Sezione di Roma, Sapienza Università di Roma, Rome, Italy
82 https://ror.org/01vj6ck58 grid.470222.1 0000 0004 7471 9712 INFN Sezione di Torino, Università di Torino, Torino, Italy; Università del Piemonte Orientale, Novara, Italy
83 grid.5133.4 0000 0001 1941 4308 INFN Sezione di Trieste, Università di Trieste, Trieste, Italy
84 https://ror.org/040c17130 grid.258803.4 0000 0001 0661 1556 Kyungpook National University, Daegu, Korea
85 https://ror.org/05kzjxq56 grid.14005.30 0000 0001 0356 9399 Chonnam National University, Institute for Universe and Elementary Particles, Kwangju, Korea
86 https://ror.org/046865y68 grid.49606.3d 0000 0001 1364 9317 Hanyang University, Seoul, Korea
87 https://ror.org/047dqcg40 grid.222754.4 0000 0001 0840 2678 Korea University, Seoul, Korea
88 https://ror.org/01zqcg218 grid.289247.2 0000 0001 2171 7818 Department of Physics, Kyung Hee University, Seoul, Korea
89 https://ror.org/00aft1q37 grid.263333.4 0000 0001 0727 6358 Sejong University, Seoul, Korea
90 https://ror.org/04h9pn542 grid.31501.36 0000 0004 0470 5905 Seoul National University, Seoul, Korea
91 https://ror.org/05en5nh73 grid.267134.5 0000 0000 8597 6969 University of Seoul, Seoul, Korea
92 https://ror.org/01wjejq96 grid.15444.30 0000 0004 0470 5454 Department of Physics, Yonsei University, Seoul, Korea
93 https://ror.org/04q78tk20 grid.264381.a 0000 0001 2181 989X Sungkyunkwan University, Suwon, Korea
94 https://ror.org/02gqgne03 grid.472279.d 0000 0004 0418 1945 College of Engineering and Technology, American University of the Middle East (AUM), Dasman, Kuwait
95 https://ror.org/00twb6c09 grid.6973.b 0000 0004 0567 9729 Riga Technical University, Riga, Latvia
96 https://ror.org/03nadee84 grid.6441.7 0000 0001 2243 2806 Vilnius University, Vilnius, Lithuania
97 https://ror.org/00rzspn62 grid.10347.31 0000 0001 2308 5949 National Centre for Particle Physics, Universiti Malaya, Kuala Lumpur, Malaysia
98 grid.11893.32 0000 0001 2193 1646 Universidad de Sonora (UNISON), Hermosillo, Mexico
99 grid.512574.0 Centro de Investigacion y de Estudios Avanzados del IPN, Mexico City, Mexico
100 https://ror.org/05vss7635 grid.441047.2 0000 0001 2156 4794 Universidad Iberoamericana, Mexico City, Mexico
101 https://ror.org/03p2z7827 grid.411659.e 0000 0001 2112 2750 Benemerita Universidad Autonoma de Puebla, Puebla, Mexico
102 https://ror.org/02drrjp49 grid.12316.37 0000 0001 2182 0188 University of Montenegro, Podgorica, Montenegro
103 grid.412621.2 0000 0001 2215 1297 National Centre for Physics, Quaid-I-Azam University, Islamabad, Pakistan
104 grid.9922.0 0000 0000 9174 1488 AGH University of Science and Technology Faculty of Computer Science, Electronics and Telecommunications, Kraków, Poland
105 https://ror.org/00nzsxq20 grid.450295.f 0000 0001 0941 0848 National Centre for Nuclear Research, Swierk, Poland
106 https://ror.org/039bjqg32 grid.12847.38 0000 0004 1937 1290 Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Warsaw, Poland
107 https://ror.org/01hys1667 grid.420929.4 Laboratório de Instrumentação e Física Experimental de Partículas, Lisbon, Portugal
108 grid.7149.b 0000 0001 2166 9385 VINCA Institute of Nuclear Sciences, University of Belgrade, Belgrade, Serbia
109 https://ror.org/05xx77y52 grid.420019.e 0000 0001 1959 5823 Centro de Investigaciones Energéticas Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain
110 https://ror.org/01cby8j38 grid.5515.4 0000 0001 1957 8126 Universidad Autónoma de Madrid, Madrid, Spain
111 https://ror.org/006gksa02 grid.10863.3c 0000 0001 2164 6351 Instituto Universitario de Ciencias y Tecnologías Espaciales de Asturias (ICTEA), Universidad de Oviedo, Oviedo, Spain
112 grid.7821.c 0000 0004 1770 272X Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria, Santander, Spain
113 https://ror.org/02phn5242 grid.8065.b 0000 0001 2182 8067 University of Colombo, Colombo, Sri Lanka
114 https://ror.org/033jvzr14 grid.412759.c 0000 0001 0103 6011 University of Ruhuna, Department of Physics, Matara, Sri Lanka
115 https://ror.org/01ggx4157 grid.9132.9 0000 0001 2156 142X CERN, European Organization for Nuclear Research, Geneva, Switzerland
116 https://ror.org/03eh3y714 grid.5991.4 0000 0001 1090 7501 Paul Scherrer Institut, Villigen, Switzerland
117 grid.5801.c 0000 0001 2156 2780 ETH Zurich-Institute for Particle Physics and Astrophysics (IPA), Zurich, Switzerland
118 https://ror.org/02crff812 grid.7400.3 0000 0004 1937 0650 Universität Zürich, Zurich, Switzerland
119 https://ror.org/00944ve71 grid.37589.30 0000 0004 0532 3167 National Central University, Chung-Li, Taiwan
120 https://ror.org/05bqach95 grid.19188.39 0000 0004 0546 0241 National Taiwan University (NTU), Taipei, Taiwan
121 https://ror.org/028wp3y58 grid.7922.e 0000 0001 0244 7875 Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok, Thailand
122 https://ror.org/05wxkj555 grid.98622.37 0000 0001 2271 3229 Physics Department, Science and Art Faculty, Çukurova University, Adana, Turkey
123 https://ror.org/014weej12 grid.6935.9 0000 0001 1881 7391 Physics Department, Middle East Technical University, Ankara, Turkey
124 https://ror.org/03z9tma90 grid.11220.30 0000 0001 2253 9056 Bogazici University, Istanbul, Turkey
125 https://ror.org/059636586 grid.10516.33 0000 0001 2174 543X Istanbul Technical University, Istanbul, Turkey
126 https://ror.org/03a5qrr21 grid.9601.e 0000 0001 2166 6619 Istanbul University, Istanbul, Turkey
127 grid.466758.e Institute for Scintillation Materials of National Academy of Science of Ukraine, Kharkiv, Ukraine
128 https://ror.org/00183pc12 grid.425540.2 0000 0000 9526 3153 National Science Centre, Kharkiv Institute of Physics and Technology, Kharkiv, Ukraine
129 https://ror.org/0524sp257 grid.5337.2 0000 0004 1936 7603 University of Bristol, Bristol, UK
130 https://ror.org/03gq8fr08 grid.76978.37 0000 0001 2296 6998 Rutherford Appleton Laboratory, Didcot, UK
131 https://ror.org/041kmwe10 grid.7445.2 0000 0001 2113 8111 Imperial College, London, UK
132 grid.7728.a 0000 0001 0724 6933 Brunel University, Uxbridge, UK
133 https://ror.org/005781934 grid.252890.4 0000 0001 2111 2894 Baylor University, Waco, TX USA
134 https://ror.org/047yk3s18 grid.39936.36 0000 0001 2174 6686 Catholic University of America, Washington, DC USA
135 https://ror.org/03xrrjk67 grid.411015.0 0000 0001 0727 7545 The University of Alabama, Tuscaloosa, AL USA
136 https://ror.org/05qwgg493 grid.189504.1 0000 0004 1936 7558 Boston University, Boston, MA USA
137 https://ror.org/05gq02987 grid.40263.33 0000 0004 1936 9094 Brown University, Providence, RI USA
138 https://ror.org/05t99sp05 grid.468726.9 0000 0004 0486 2046 University of California, Davis, Davis, CA USA
139 grid.19006.3e 0000 0000 9632 6718 University of California, Los Angeles, CA USA
140 https://ror.org/05t99sp05 grid.468726.9 0000 0004 0486 2046 University of California, Riverside, Riverside, CA USA
141 https://ror.org/05t99sp05 grid.468726.9 0000 0004 0486 2046 University of California, San Diego, La Jolla, CA USA
142 grid.133342.4 0000 0004 1936 9676 Department of Physics, University of California, Santa Barbara, Santa Barbara, CA USA
143 https://ror.org/05dxps055 grid.20861.3d 0000 0001 0706 8890 California Institute of Technology, Pasadena, CA USA
144 https://ror.org/05x2bcf33 grid.147455.6 0000 0001 2097 0344 Carnegie Mellon University, Pittsburgh, PA USA
145 https://ror.org/02ttsq026 grid.266190.a 0000 0000 9621 4564 University of Colorado Boulder, Boulder, CO USA
146 https://ror.org/05bnh6r87 grid.5386.8 0000 0004 1936 877X Cornell University, Ithaca, NY USA
147 https://ror.org/020hgte69 grid.417851.e 0000 0001 0675 0679 Fermi National Accelerator Laboratory, Batavia, IL USA
148 https://ror.org/02y3ad647 grid.15276.37 0000 0004 1936 8091 University of Florida, Gainesville, FL USA
149 https://ror.org/05g3dte14 grid.255986.5 0000 0004 0472 0419 Florida State University, Tallahassee, FL USA
150 https://ror.org/04atsbb87 grid.255966.b 0000 0001 2229 7296 Florida Institute of Technology, Melbourne, FL USA
151 https://ror.org/02mpq6x41 grid.185648.6 0000 0001 2175 0319 University of Illinois at Chicago (UIC), Chicago, IL USA
152 https://ror.org/036jqmy94 grid.214572.7 0000 0004 1936 8294 The University of Iowa, Iowa City, IA USA
153 https://ror.org/00za53h95 grid.21107.35 0000 0001 2171 9311 Johns Hopkins University, Baltimore, MD USA
154 https://ror.org/001tmjg57 grid.266515.3 0000 0001 2106 0692 The University of Kansas, Lawrence, KS USA
155 https://ror.org/05p1j8758 grid.36567.31 0000 0001 0737 1259 Kansas State University, Manhattan, KS USA
156 https://ror.org/041nk4h53 grid.250008.f 0000 0001 2160 9702 Lawrence Livermore National Laboratory, Livermore, CA USA
157 https://ror.org/047s2c258 grid.164295.d 0000 0001 0941 7177 University of Maryland, College Park, MD USA
158 https://ror.org/042nb2s44 grid.116068.8 0000 0001 2341 2786 Massachusetts Institute of Technology, Cambridge, MA USA
159 https://ror.org/017zqws13 grid.17635.36 0000 0004 1936 8657 University of Minnesota, Minneapolis, MN USA
160 https://ror.org/02teq1165 grid.251313.7 0000 0001 2169 2489 University of Mississippi, Oxford, MS USA
161 https://ror.org/043mer456 grid.24434.35 0000 0004 1937 0060 University of Nebraska-Lincoln, Lincoln, NE USA
162 grid.273335.3 0000 0004 1936 9887 State University of New York at Buffalo, Buffalo, NY USA
163 https://ror.org/04t5xt781 grid.261112.7 0000 0001 2173 3359 Northeastern University, Boston, MA USA
164 https://ror.org/000e0be47 grid.16753.36 0000 0001 2299 3507 Northwestern University, Evanston, IL USA
165 https://ror.org/00mkhxb43 grid.131063.6 0000 0001 2168 0066 University of Notre Dame, Notre Dame, IN USA
166 https://ror.org/00rs6vg23 grid.261331.4 0000 0001 2285 7943 The Ohio State University, Columbus, OH USA
167 https://ror.org/00hx57361 grid.16750.35 0000 0001 2097 5006 Princeton University, Princeton, NJ USA
168 https://ror.org/00wek6x04 grid.267044.3 0000 0004 0398 9176 University of Puerto Rico, Mayaguez, PR USA
169 https://ror.org/02dqehb95 grid.169077.e 0000 0004 1937 2197 Purdue University, West Lafayette, IN USA
170 https://ror.org/04keq6987 grid.504659.b 0000 0000 8864 7239 Purdue University Northwest, Hammond, IN USA
171 https://ror.org/008zs3103 grid.21940.3e 0000 0004 1936 8278 Rice University, Houston, TX USA
172 https://ror.org/022kthw22 grid.16416.34 0000 0004 1936 9174 University of Rochester, Rochester, NY USA
173 https://ror.org/0420db125 grid.134907.8 0000 0001 2166 1519 The Rockefeller University, New York, NY USA
174 https://ror.org/05vt9qd57 grid.430387.b 0000 0004 1936 8796 Rutgers, The State University of New Jersey, Piscataway, NJ USA
175 https://ror.org/020f3ap87 grid.411461.7 0000 0001 2315 1184 University of Tennessee, Knoxville, TN USA
176 https://ror.org/01f5ytq51 grid.264756.4 0000 0004 4687 2082 Texas A &M University, College Station, TX USA
177 grid.264784.b 0000 0001 2186 7496 Texas Tech University, Lubbock, TX USA
178 https://ror.org/02vm5rt34 grid.152326.1 0000 0001 2264 7217 Vanderbilt University, Nashville, TN USA
179 https://ror.org/0153tk833 grid.27755.32 0000 0000 9136 933X University of Virginia, Charlottesville, VA USA
180 https://ror.org/01070mq45 grid.254444.7 0000 0001 1456 7807 Wayne State University, Detroit, MI USA
181 https://ror.org/01y2jtd41 grid.14003.36 0000 0001 2167 3675 University of Wisconsin-Madison, Madison, WI USA
182 grid.9132.9 0000 0001 2156 142X Authors affiliated with an institute or an international laboratory covered by a cooperation agreement with CERN, Geneva, Switzerland
183 https://ror.org/00s8vne50 grid.21072.36 0000 0004 0640 687X Yerevan State University, Yerevan, Armenia
184 https://ror.org/04d836q62 grid.5329.d 0000 0004 1937 0669 TU Wien, Vienna, Austria
185 grid.442567.6 0000 0000 9015 5153 Institute of Basic and Applied Sciences, Faculty of Engineering, Arab Academy for Science, Technology and Maritime Transport, Alexandria, Egypt
186 https://ror.org/01r9htc13 grid.4989.c 0000 0001 2348 6355 Université Libre de Bruxelles, Bruxelles, Belgium
187 https://ror.org/04wffgt70 grid.411087.b 0000 0001 0723 2494 Universidade Estadual de Campinas, Campinas, Brazil
188 https://ror.org/041yk2d64 grid.8532.c 0000 0001 2200 7498 Federal University of Rio Grande do Sul, Porto Alegre, Brazil
189 grid.412352.3 0000 0001 2163 5978 UFMS, Nova Andradina, Brazil
190 https://ror.org/05qbk4x57 grid.410726.6 0000 0004 1797 8419 University of Chinese Academy of Sciences, Beijing, China
191 https://ror.org/036trcv74 grid.260474.3 0000 0001 0089 5711 Nanjing Normal University, Nanjing, China
192 https://ror.org/036jqmy94 grid.214572.7 0000 0004 1936 8294 Now at The University of Iowa, Iowa City, IA USA
193 https://ror.org/05qbk4x57 grid.410726.6 0000 0004 1797 8419 University of Chinese Academy of Sciences, Beijing, China
194 grid.9132.9 0000 0001 2156 142X An institute or an international laboratory covered by a cooperation agreement with CERN, Geneva, Switzerland
195 grid.440862.c 0000 0004 0377 5514 Now at British University in Egypt, Cairo, Egypt
196 https://ror.org/03q21mh05 grid.7776.1 0000 0004 0639 9286 Now at Cairo University, Cairo, Egypt
197 https://ror.org/02dqehb95 grid.169077.e 0000 0004 1937 2197 Purdue University, West Lafayette, IN USA
198 https://ror.org/04k8k6n84 grid.9156.b 0000 0004 0473 5039 Université de Haute Alsace, Mulhouse, France
199 https://ror.org/03cve4549 grid.12527.33 0000 0001 0662 3178 Department of Physics, Tsinghua University, Beijing, China
200 https://ror.org/051qn8h41 grid.428923.6 0000 0000 9489 2441 Ilia State University, Tbilisi, Georgia
201 https://ror.org/04j5z3x06 grid.412290.c 0000 0000 8024 0602 The University of the State of Amazonas, Manaus, Brazil
202 grid.412176.7 0000 0001 1498 7262 Erzincan Binali Yildirim University, Erzincan, Turkey
203 https://ror.org/00g30e956 grid.9026.d 0000 0001 2287 2617 University of Hamburg, Hamburg, Germany
204 https://ror.org/04xfq0f34 grid.1957.a 0000 0001 0728 696X III. Physikalisches Institut A, RWTH Aachen University, Aachen, Germany
205 grid.411751.7 0000 0000 9908 3264 Isfahan University of Technology, Isfahan, Iran
206 grid.7787.f 0000 0001 2364 5811 Bergische University Wuppertal (BUW), Wuppertal, Germany
207 https://ror.org/02wxx3e24 grid.8842.6 0000 0001 2188 0404 Brandenburg University of Technology, Cottbus, Germany
208 https://ror.org/02nv7yv05 grid.8385.6 0000 0001 2297 375X Forschungszentrum Jülich, Juelich, Germany
209 https://ror.org/01ggx4157 grid.9132.9 0000 0001 2156 142X CERN, European Organization for Nuclear Research, Geneva, Switzerland
210 https://ror.org/01jaj8n65 grid.252487.e 0000 0000 8632 679X Physics Department, Faculty of Science, Assiut University, Assiut, Egypt
211 Karoly Robert Campus, MATE Institute of Technology, Gyongyos, Hungary
212 https://ror.org/035dsb084 grid.419766.b 0000 0004 1759 8344 Wigner Research Centre for Physics, Budapest, Hungary
213 https://ror.org/02xf66n48 grid.7122.6 0000 0001 1088 8582 Institute of Physics, University of Debrecen, Debrecen, Hungary
214 grid.418861.2 0000 0001 0674 7808 Institute of Nuclear Research ATOMKI, Debrecen, Hungary
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221 grid.34980.36 0000 0001 0482 5067 Indian Institute of Science (IISc), Bangalore, India
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241 https://ror.org/059ex5q34 grid.418270.8 0000 0004 0428 7635 Consejo Nacional de Ciencia y Tecnología, Mexico City, Mexico
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247 grid.443373.4 0000 0001 0438 3334 Trincomalee Campus, Eastern University, Sri Lanka, Nilaveli, Sri Lanka
248 grid.8982.b 0000 0004 1762 5736 INFN Sezione di Pavia, Università di Pavia, Pavia, Italy
249 https://ror.org/04gnjpq42 grid.5216.0 0000 0001 2155 0800 National and Kapodistrian University of Athens, Athens, Greece
250 https://ror.org/02s376052 grid.5333.6 0000 0001 2183 9049 Ecole Polytechnique Fédérale Lausanne, Lausanne, Switzerland
251 https://ror.org/02crff812 grid.7400.3 0000 0004 1937 0650 Universität Zürich, Zurich, Switzerland
252 https://ror.org/05kdjqf72 grid.475784.d 0000 0000 9532 5705 Stefan Meyer Institute for Subatomic Physics, Vienna, Austria
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254 Near East University, Research Center of Experimental Health Science, Mersin, Turkey
255 https://ror.org/02s82rs08 grid.505922.9 Konya Technical University, Konya, Turkey
256 https://ror.org/017v96566 0000 0004 6412 5697 Izmir Bakircay University, Izmir, Turkey
257 https://ror.org/02s4gkg68 grid.411126.1 0000 0004 0369 5557 Adiyaman University, Adiyaman, Turkey
258 https://ror.org/05msvfx67 grid.465940.a 0000 0004 0520 0861 Istanbul Gedik University, Istanbul, Turkey
259 https://ror.org/013s3zh21 grid.411124.3 0000 0004 1769 6008 Necmettin Erbakan University, Konya, Turkey
260 grid.411743.4 0000 0004 0369 8360 Bozok Universitetesi Rektörlügü, Yozgat, Turkey
261 https://ror.org/02kswqa67 grid.16477.33 0000 0001 0668 8422 Marmara University, Istanbul, Turkey
262 https://ror.org/010t24d82 grid.510982.7 Milli Savunma University, Istanbul, Turkey
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264 grid.506076.2 0000 0004 1797 5496 Faculty of Engineering, Istanbul University-Cerrahpasa, Istanbul, Turkey
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266 https://ror.org/006e5kg04 grid.8767.e 0000 0001 2290 8069 Vrije Universiteit Brussel, Brussel, Belgium
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268 https://ror.org/0524sp257 grid.5337.2 0000 0004 1936 7603 University of Bristol, Bristol, UK
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270 https://ror.org/02bfwt286 grid.1002.3 0000 0004 1936 7857 Faculty of Science, Monash University, Clayton, Australia
271 grid.7605.4 0000 0001 2336 6580 Università di Torino, Turin, Italy
272 https://ror.org/02faxbd19 grid.418297.1 0000 0000 8888 5173 Bethel University, St. Paul, MN USA
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278 https://ror.org/00aamz256 grid.41405.34 0000 0001 0702 1187 Georgian Technical University, Tbilisi, Georgia
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280 https://ror.org/047g8vk19 grid.411739.9 0000 0001 2331 2603 Erciyes University, Kayseri, Turkey
281 https://ror.org/03x8rhq63 grid.450259.f 0000 0004 1804 2516 Institute of Modern Physics and Key Laboratory of Nuclear Physics and Ion-beam Application (MOE)-Fudan University, Shanghai, China
282 https://ror.org/03vb4dm14 grid.412392.f 0000 0004 0413 3978 Texas A &M University at Qatar, Doha, Qatar
283 https://ror.org/040c17130 grid.258803.4 0000 0001 0661 1556 Kyungpook National University, Daegu, Korea
284 grid.9132.9 0000 0001 2156 142X another institute or international laboratory covered by a cooperation agreement with CERN, Geneva, Switzerland
285 https://ror.org/00ad27c73 grid.48507.3e 0000 0004 0482 7128 Yerevan Physics Institute, Yerevan, Armenia
286 https://ror.org/041kmwe10 grid.7445.2 0000 0001 2113 8111 Imperial College, London, UK
287 grid.443859.7 0000 0004 0477 2171 Institute of Nuclear Physics of the Uzbekistan Academy of Sciences, Tashkent, Uzbekistan
288 grid.9132.9 0000 0001 2156 142X CERN, 1211 Geneva 23, Switzerland
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Funded by SCOAP3. SCOAP3 supports the goals of the International Year of Basic Sciences for Sustainable Development.
The strange quark content of the proton is probed through the measurement of the production cross section for a W boson and a charm (c) quark in proton–proton collisions at a center-of-mass energy of 13TeV. The analysis uses a data sample corresponding to a total integrated luminosity of 138fb-1 collected with the CMS detector at the LHC. The W bosons are identified through their leptonic decays to an electron or a muon, and a neutrino. Charm jets are tagged using the presence of a muon or a secondary vertex inside the jet. The W+c production cross section and the cross section ratio Rc±=σ(W++c¯)/σ(W-+c) are measured inclusively and differentially as functions of the transverse momentum and the pseudorapidity of the lepton originating from the W boson decay. The precision of the measurements is improved with respect to previous studies, reaching 1% in Rc±=0.950±0.005(stat)±0.010(syst). The measurements are compared with theoretical predictions up to next-to-next-to-leading order in perturbative quantum chromodynamics.

SCScience Committee Tumasyan A. http://dx.doi.org/10.13039/501100013699 Austrian Federal Ministry of Education, Science and Research BMBWF (Bundesministerium für Bildung, Wissenschaft, Forschung) [name change from BMWFW] Adam W. http://dx.doi.org/10.13039/501100002428 Austrian Science Fund FWF Andrejkovic J. W. http://dx.doi.org/10.13039/501100002661 Belgian Fonds de la Recherche Scientifique FRS – FNRS Bergauer T. http://dx.doi.org/10.13039/501100003130 Belgian Fonds voor Wetenschappelijk Onderzoek FWO Chatterjee S. http://dx.doi.org/10.13039/501100003593 CNPq Conselho Nacional de Desenvolvimento Cientifico e Tecnelógica Damanakis K. http://dx.doi.org/10.13039/501100002322 CAPES Coordenação de Aperfeiçoamento de Pessoal de Nível Superior Dragicevic M. http://dx.doi.org/10.13039/501100004586 FAPERJ Fundação de Amparo à Pesquisa do Estado de Rio de Janeiro Valle A. Escalante Del http://dx.doi.org/10.13039/501100004263 FAPERGS Fundação de Amparo À Pesquisa do Estado do Rio Grande do Sul Hussain P. S. http://dx.doi.org/10.13039/501100001807 FAPESP Fundação de Amparo à Pesquisa do Estado de São Paulo Jeitler M. http://dx.doi.org/10.13039/501100005992 Bulgarian Ministry of Education and Science MES Krammer N. http://dx.doi.org/10.13039/501100003336 Bulgarian National Science Fund BNSF Lechner L. http://dx.doi.org/10.13039/100012470 CERN CERN [Conseil Européen pour la Recherche Nucléaire] Liko D. http://dx.doi.org/10.13039/501100002367 Chinese Academy of Sciences CAS Mikulec I. http://dx.doi.org/10.13039/501100002855 Ministry of Science and Technology MOST Paulitsch P. http://dx.doi.org/10.13039/501100001809 Chinese National Natural Science Foundation of China NSFC Pitters F. M. http://dx.doi.org/10.13039/100007637 Colombian Funding Agency (MINICIENCIAS) Departamento Administriva de Ciencia, Tecnología e Innovación, now Ministerio de Ciencia Tecnología e Innovación Schieck J. http://dx.doi.org/10.13039/501100006588 Croatian Ministry of Science, Education and Sport Ministarstvo Znanosti, Obrazovanja i Sporta; MSES Schöfbeck R. http://dx.doi.org/10.13039/501100004488 Croatian Science Foundation Hrvatska Zaklada za Znanost; CSF Schwarz D. http://dx.doi.org/10.13039/501100001810 Research and Innovation Foundation RIF Sonawane M. http://dx.doi.org/10.13039/501100004299 SENESCYT Secretaría de Educación Superior, Ciencia, Tecnología e Innovación Templ S. http://dx.doi.org/10.13039/501100003510 Ministry of Education and Research Haridus- ja Teadusministeerium; MoER Waltenberger W. http://dx.doi.org/10.13039/501100002301 Estonian Research Council via PRG780, PRG803, and PRG445 Eesti Teadusagentuur; ERC IUT Wulz C.-E. http://dx.doi.org/10.13039/501100008530 European Regional Development Fund ERDF Darwish M. R. http://dx.doi.org/10.13039/501100002341 Academy of Finland Suomen Akatemia Janssen T. Finnish Ministry of Education and CultureMEC Kello T. Helsinki Institute of PhysicsHIP Sfar H. Rejeb http://dx.doi.org/10.13039/501100004794 Institut National de Physique Nucléaire et de Physique des Particules IN2P3 Mechelen P. Van http://dx.doi.org/10.13039/501100004794 Centre National de la Recherche Scientifique CNRS Bols E. S. http://dx.doi.org/10.13039/501100006489 Commissariat à l’Énergie Atomique et aux Énergies Alternatives CEA D’Hondt J. http://dx.doi.org/10.13039/501100002347 Bundesministerium für Bildung und Forschung BMBF De Moor A. http://dx.doi.org/10.13039/501100001659 Deutsche Forschungsgemeinschaft DFG Delcourt M. http://dx.doi.org/10.13039/501100001656 Helmholtz-Gemeinschaft Deutscher Forschungszentren HGF Faham H. El http://dx.doi.org/10.13039/501100003448 General Secretariat for Research and Innovation GSRI Lowette S. http://dx.doi.org/10.13039/501100011019 National Research, Development and Innovation Office NKFIH: Nemzeti Kutatási, Fejlesztési és Innováció Hivatal Moortgat S. http://dx.doi.org/10.13039/501100001502 Department of Atomic Energy DAE Morton A. http://dx.doi.org/10.13039/501100001409 Department of Science and Technology DST Müller D. http://dx.doi.org/10.13039/501100006115 Institute for Research in Fundamental Studies IPM Sahasransu A. R. http://dx.doi.org/10.13039/501100001602 Science Foundation SFI Tavernier S. http://dx.doi.org/10.13039/501100004007 Istituto Nazionale di Fisica Nucleare INFN Doninck W. Van http://dx.doi.org/10.13039/501100004085 Korean Ministry of Education, Science and Technology previously listed was MSIP, Ministry of Science, ICT, and Future Planning Vannerom D. http://dx.doi.org/10.13039/501100003725 National Research Foundation of Korea (NRF) previously listed was WCU (World Class University) Clerbaux B. http://dx.doi.org/10.13039/501100001864 MES Ministry of Education and Science De Lentdecker G. http://dx.doi.org/10.13039/501100008523 Lithuanian Academy of Sciences LAS or Lietuvos Mokslu Akademija Favart L. http://dx.doi.org/10.13039/501100003093 Ministry of Education ?Ministry of Higher Education, Malaysia Hohov D. http://dx.doi.org/10.13039/501100004386 University of Malaya http://dx.doi.org/10.13039/501100006348 BUAP Benemérita Universidad Autónoma de Puebla Lee K. http://dx.doi.org/10.13039/501100008688 CINVESTAV Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional Mahdavikhorrami M. http://dx.doi.org/10.13039/501100003141 CONACYT Consejo Nacional de Ciencia y Tecnología Makarenko I. LNSLaboratorio Nacional de Supercómputo del Sureste Malara A. http://dx.doi.org/10.13039/100010096 SEP Secretaría de Educación Pública Paredes S. http://dx.doi.org/10.13039/501100005324 UASLP Universidad Autónoma de San Luis Potosí Pétré L. MOSMinistry of Science Postiau N. http://dx.doi.org/10.13039/501100003524 Ministry of Business, Innovation and Employment MBIE Thomas L. http://dx.doi.org/10.13039/501100008689 Pakistan Atomic Energy Commission PAEC Bemden M. Vanden http://dx.doi.org/10.13039/501100004569 Ministry of Educaton and Science Ministerstwo Edukacji I Nauki; MES [was MSHE, Ministerstwo Nauki i Szkolnictwa Wyzszego] Velde C. Vander http://dx.doi.org/10.13039/501100004442 National Science Centre Narodowe Centrum Nauki; NSC Vanlaer P. http://dx.doi.org/10.13039/501100001871 Fundação para a Ciência e a Tecnologia, CERN/FIS-PAR/0025/2019 and CERN/FIS-INS/0032/2019 FCT Dobur D. http://dx.doi.org/10.13039/501100003822 JINR, Dubna Joint Institute for Nuclear Research Knolle J. http://dx.doi.org/10.13039/501100003443 Ministry of Education and Science of the Russian Federation MON Lambrecht L. http://dx.doi.org/10.13039/501100008687 Federal Agency of Atomic Energy of the Russian Federation RosAtom Mestdach G. http://dx.doi.org/10.13039/501100002674 Russian Academy of Sciences RAS Rendón C. http://dx.doi.org/10.13039/501100002261 Russian Foundation for Basic Research RFBR Samalan A. http://dx.doi.org/10.13039/501100013400 National Research Center “Kurchatov Institute” NRC KI Skovpen K. http://dx.doi.org/10.13039/501100004564 Ministry of Education, Science and Technological Development of Serbia MESTD Tytgat M. http://dx.doi.org/10.13039/501100011033 MCIN/AEI/10.13039/501100011033, ERDF “a way of making Europe” MCIN/AEI (Ministerio de Ciencia e Innovación/Agencia Estatal de Investigación) Bossche N. Van Den http://dx.doi.org/10.13039/501100008530 Fondo Europeo de Desarrollo Regional, Spain FEDER (ERDF) Vermassen B. https://doi.org/10.13039/100011941 Plan de Ciencia, Tecnología e Innovación del Principado de Asturias PCTI Wezenbeek L. http://dx.doi.org/10.13039/501100008981 MOSTR Ministry of Science, Technology, and Research Benecke A. ETH BoardEidgenössische Technische Hochschule (ETH) Zürich Bruno G. http://dx.doi.org/10.13039/501100003006 ETH Zurich Eidgenössische Technische Hochschule (ETH) Zürich Bury F. http://dx.doi.org/10.13039/501100004219 PSI Paul Scherrer Institut Caputo C. http://dx.doi.org/10.13039/501100001711 SNF Swiss National Science Foundation (Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung) David P. UniZHUniversität Zürich Delaere C. Canton ZurichSERState Secretariat for Education and Research (Education, Research, and Innovation: SERI) Giammanco A. http://dx.doi.org/10.13039/501100004663 Ministry of Science and Technology Thailand Center of Excellence in PhysicsInstitute for the Promotion of Teaching Science and Technology of ThailandSpecial Task Force for Activating Researchhttp://dx.doi.org/10.13039/501100004192 National Science and Technology Development Agency of Thailand http://dx.doi.org/10.13039/501100004410 Scientific and Technical Research Council of Turkey Türkiye Bilimsel ve Teknolojik Arastirma Kurumu Tran T. T. http://dx.doi.org/10.13039/100010440 Turkish Atomic Energy Authority Türkiye Atom Enerjisi Kurumu Vischia P. http://dx.doi.org/10.13039/501100004742 National Academy of Sciences of Ukraine http://dx.doi.org/10.13039/501100000271 Science and Technology Facilities Council http://dx.doi.org/10.13039/100000015 US Department of Energy http://dx.doi.org/10.13039/100000001 US National Science Foundation Marie-Curie programmehttp://dx.doi.org/10.13039/501100000781 European Research Council and EPLANET (European Union) ERC doi only Adam W. http://dx.doi.org/10.13039/501100000921 European Research Council/European Cooperation in Science and Technology), Action CA16108 COST Andrejkovic J. W. http://dx.doi.org/10.13039/100010661 Horizon 2020 Grant, contract Nos. 675440, 724704, 752730, 758316, 765710, 824093, 884104, 683211 (European Union) http://dx.doi.org/10.13039/501100004117 Leventis Foundation http://dx.doi.org/10.13039/100000879 Alfred P. Sloan Foundation http://dx.doi.org/10.13039/100005156 Alexander von Humboldt Foundation Alexander von Humboldt-Stiftung Dragicevic M. Science Committee, project no. 22rl-037Belgian Federal Science Policy Officehttp://dx.doi.org/10.13039/501100003134 Fonds pour la Formation à la Recherche dans l’Industrie et dans l’Agriculture (FRIA-Belgium) http://dx.doi.org/10.13039/501100003132 Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium) http://dx.doi.org/10.13039/501100002661 Belgian Fonds de la Recherche Scientifique, “Excellence of Science - EOS” - be.h project n. 30820817 FRS – FNRS Lechner L. http://dx.doi.org/10.13039/501100003130 Belgian Fonds voor Wetenschappelijk Onderzoek, “Excellence of Science - EOS” - be.h project n. 30820817 FWO Liko D. http://dx.doi.org/10.13039/501100009592 Beijing Municipal Science & Technology Commission, No. Z191100007219010 http://dx.doi.org/10.13039/501100001823 Ministry of Education, Youth and Sports (MEYS) of the Czech Republic Ministerstvo Školství, Mládeže a Telovýchovy Paulitsch P. http://dx.doi.org/10.13039/501100004801 Shota Rustaveli National Science Foundation SRNSF Pitters F. M. http://dx.doi.org/10.13039/501100001659 Deutsche Forschungsgemeinschaft (DFG) under Germany’s Excellence Strategy – EXC 2121 “Quantum Universe” – 390833306 http://dx.doi.org/10.13039/501100001659 Deutsche Forschungsgemeinschaft (DFG), project numbers 400140256 - GRK2497, RTG2044, INST 39/963-1 FUGG (bwForCluster NEMO) ; 396021762 – TRR 257: P3H http://dx.doi.org/10.13039/501100003542 Ministry of Science, Research and Art Baden-Württemberg, through bwHPC http://dx.doi.org/10.13039/501100013209 Hellenic Foundation for Research and Innovation, Project Number 2288 HFRI Sonawane M. http://dx.doi.org/10.13039/501100003825 Hungarian Academy of Sciences Magyar Tudományos Akadémia Templ S. http://dx.doi.org/10.13039/501100011019 New National Excellence Program - ÚNKP, the NKFIH research grants K 124845, K 124850, K 128713, K 128786, K 129058, K 131991, K 133046, K 138136, K 143460, K 143477, 2020-2.2.1-ED-2021-00181, and TKP2021-NKTA-64 ÚNKP: Új Nemzeti Kiválósági Program Waltenberger W. 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pmcIntroduction

The associated production of a W boson and a single charm (c) quark (W+c) in proton–proton (pp) collisions at the CERN LHC is directly sensitive to the strange quark (s) content of the colliding protons at an energy scale of the order of the W  boson mass [1]. This sensitivity comes from the dominance of the sg→W+c contribution over the Cabibbo-suppressed process dg→W+c at tree level (see Fig. 1). Therefore, this process provides valuable information on the strange quark parton distribution function (PDF), which is one of the least constrained PDFs of the proton. Accurate measurements of the W+c production cross section and of the Rc±=σ(W++c¯)/σ(W-+c) cross section ratio can be used to further constrain the strange quark PDF, and to probe the level of asymmetry between the s and s¯ PDFs [2–4].

Furthermore, the production of W+c events provides a useful calibration sample for the measurements and searches at the LHC involving electroweak bosons and c  quarks in the final state [5, 6]. Precise measurements of W+c production can be used to check the theoretical calculations of this process and its modeling in the currently available Monte Carlo (MC) event generators.

The W+c production in pp collisions at the LHC has been reported by the CMS [7–9], ATLAS [10, 11], and LHCb [12] Collaborations at center-of-mass energies s=7, 8, and 13TeV. Measurements of W+c fiducial cross sections and the Rc± cross section ratio were performed in those analyses by identifying charm events through the reconstruction of exclusive decays of charm hadrons, or finding secondary vertices or muons inside a jet.Fig. 1 Leading order Feynman diagrams for the associated production of a W boson and a charm quark. The electric charges of the W boson and c  quark have opposite signs

In this paper, we present a measurement of the W+c production cross section and cross section ratio Rc± at s=13TeV using the data collected in 2016–2018. The precision is improved compared with previous CMS measurements. In particular, the uncertainty in the Rc± measurement is halved, reaching a precision of 1%. Measurements are performed in four independent channels, depending on the method used for identifying the c  quarks and the W boson decay mode (electron or muon). Jets are tagged as originating from the hadronization of c  quarks (c jet) by the presence of either muons or secondary vertices inside the jets. The combination of the measurements in the four channels, the use of the large data set collected at s=13TeV, and the reduction of systematic uncertainties, lead to more precise measurements.

A key property of W+c production is the opposite sign of the electric charges of the W boson and c  quark. This feature allows the suppression of most of the background events, which exhibit bottom or charm quarks and antiquarks with equal probability and identical kinematics, such as top quark-antiquark or W+cc¯ production. The statistical subtraction of the distributions of physical observables for events where the reconstructed charges of the W boson and the c  quark have opposite sign (OS) and same sign (SS) leads to the effective removal of these backgrounds [7, 8]. This technique, referred to as OS-SS subtraction, enhances the sensitivity to the sg→W+c process, and therefore to the strange quark PDF.

The OS-SS cross sections σ(W++c¯)≡σ(pp→W++c¯)B(W+→ℓ+ν), σ(W-+c)≡σ(pp→W-+c)B(W-→ℓ-ν¯) (where B denotes the branching fraction), their sum σ(W+c)≡σ(W++c¯)+σ(W-+c), and the cross section ratio Rc±≡σ(W++c¯)/σ(W-+c) are measured. Inclusive and differential cross sections are measured as functions of the transverse momentum (pTℓ) and pseudorapidity (ηℓ) of the lepton from the W boson decay. Measurements are unfolded to the particle and parton levels both in a fiducial region of phase space defined in terms of the kinematics of the lepton from the W boson (pTℓ>35GeV, |ηℓ|<2.4) and of the c jet (pTc jet>30GeV, |ηc jet|<2.4).

The theoretical cross section for W+c production at the LHC [13] is well known at the next-to-leading order (NLO) accuracy in perturbative quantum chromodynamics (QCD). Recently, the first computation of next-to-NLO (NNLO) QCD corrections was published [14, 15]. The measurements presented here are compared with the predictions of these NNLO QCD calculations, which include NLO electroweak (EW) corrections. The measurements are also compared with the predictions of the parton-level MC program MCFM [16], which implements calculations at NLO in QCD using several proton PDF sets.

The paper is structured as follows: the CMS detector is briefly described in Sect. 2, and the data and simulated samples used are presented in Sect. 3. Sections 4 and 5 describe the physics object reconstruction and the selection of the W+c signal sample. Section 6 reviews the most important sources of systematic uncertainties and their impact on the measurements. Cross section and cross section ratio measurements, compared with the NLO QCD theoretical predictions using different PDF sets, are detailed in Sect. 7. The comparisons of the measurements with the NNLO QCD calculations are presented in Sect. 8. The main results of the paper are summarized in Sect. 9.

Tabulated results are provided in HEPData [17].

The CMS detector

The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the magnetic volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter (HCAL), each composed of a barrel and two endcap sections. Additional forward calorimetry complements the coverage provided by the barrel and endcap detectors. The silicon tracker measures charged particles within the pseudorapidity range |η|<2.5. For nonisolated particles of 1<pT<10GeV and |η|<1.4, the track resolutions are typically 1.5% in pT and 20–75 μm in the transverse impact parameter [18]. The upgrade of the pixel tracking detector [19] in early 2017, which includes additional layers and places the innermost layer closer to the interaction point, significantly improves the performance of heavy-flavor jet identification [20]. Muons are measured in the pseudorapidity range |η|<2.4, with detection planes made using three technologies: drift tubes, cathode strip chambers, and resistive plate chambers. A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, is reported in Ref. [21].

Events of interest are selected using a two-tiered trigger system. The first level, composed of custom hardware processors, uses information from the calorimeters and muon detectors to select events at a rate of around 100 kHz within a fixed latency of about 4 μs [22]. The second level, known as the high-level trigger, consists of a farm of processors running a version of the full event reconstruction software optimized for fast processing, and reduces the event rate to around 1 kHz before data storage [23].

Data and simulated samples

This analysis is performed using a data sample of pp collisions at s=13TeV collected by the CMS experiment during the 2016 (36.3fb-1), 2017 (41.5fb-1), and 2018 (59.8fb-1) data-taking periods with a total integrated luminosity of 138fb-1.

The experimental signature of the signal events, an isolated high-pT lepton together with a c jet, is also present in other background processes. Sources of background include top quark production (tt¯ and single top quark), diboson (WW, WZ, and ZZ) processes (collectively denoted as VV), the production of a Zboson (or a virtual photon) in association with jets (Z+jets), and W+cc¯ or W+bb¯ events.

Samples of signal and background events are simulated using MC event generators based on fixed-order perturbative QCD calculations, supplemented with parton showering and multiparton interactions. Simulated samples of W+jets and Z+jets events are produced at NLO accuracy with the MadGraph5_amc@nlo [24] (version 2.6.3) matrix element generator with up to two partons in the final state. The decay of the W and Zbosons to tau leptons is included in the W+jets and Z+jets simulations. Samples of tt¯ and single top (s-, t-, and tW channels) events are generated at NLO accuracy with powheg v2.0 [25]. The cross sections for W+jets, Z+jets, tt¯, and single top production are obtained at NNLO in QCD [26, 27]. The diboson production is modeled with samples of events generated with pythia8 [28] (version 8.219).

The simulated W+jets sample is composed of W bosons accompanied by jets originating from quarks of all flavors and gluons. Simulated W+jets events are classified according to the flavor of the outgoing generated partons as: (i) W+b if at least one bottom quark was generated in the hard process; (ii) W+c if a single charm quark was created in the hard process; (iii) W+cc¯ if a cc¯ pair was present in the event; (iv) W+udsg if no c  or b  quarks were produced.

Data collected in different running periods are modeled with specific simulation configurations. For simulations corresponding to 2016 detector conditions, the NLO NNPDF3.0 [29] PDF set is used, whereas the MC samples for 2017–2018 make use of the NNLO NNPDF3.1 [30] PDF set. The parton showering, hadronization, and the underlying events are modeled by pythiav8.212 (v8.230) using the CUETP8M1 [31, 32] (CP5 [33]) tune for the 2016 (2017–2018) samples. The jet matching and merging scheme for the MadGraph5_amc@nlo samples is FxFx [34].

In the pythia8 simulations, the charm fragmentation fractions, defined as the probabilities for c  quarks to hadronize as particular charm hadrons, corresponding to D±, D0/D¯0, Ds± and Λc± hadrons, are corrected to match those in Ref. [35]. In addition, the leptonic and hadronic decay branching fractions of those hadrons are corrected to agree with more recent measurements [36].

Generated events are processed through a full Geant4-based [37] CMS detector simulation and trigger emulation. Simulated events are reconstructed with the same algorithms used to reconstruct collision data.

The simulated samples incorporate additional pp interactions in the same or nearby bunch crossings (pileup) to reproduce the experimental conditions. Simulated events are weighted so the pileup distribution matches the experimental data.

Object reconstruction

The global event reconstruction (also called particle-flow event reconstruction [38]) reconstructs and identifies each individual particle in an event, with an optimized combination of all subdetector information. In this process, the identification of the particle type (photon, electron, muon, charged or neutral hadron) plays an important role in the determination of the particle direction and energy. Photons are identified as ECAL energy clusters not linked to the extrapolation of any charged-particle trajectory. Electrons are identified as a primary charged-particle track and with many ECAL energy clusters corresponding to this track extrapolation to the ECAL and to possible bremsstrahlung photons emitted along the path through the tracker material. Muons are identified as tracks in the central tracker consistent with either a track or several hits in the muon system, and associated with calorimeter deposits compatible with the muon hypothesis. Charged hadrons are identified as charged particle tracks neither identified as electrons nor as muons. Finally, neutral hadrons are identified as HCAL energy clusters not linked to any charged-hadron trajectory, or as a combined ECAL and HCAL energy excess with respect to the expected charged-hadron energy deposit.

The primary vertex (PV) is taken to be the vertex corresponding to the hardest scattering in the event, evaluated using tracking information alone, as described in Section 9.4.1 of Ref. [39].

The energy of photons is obtained from the ECAL measurement. The energy of electrons is determined from a combination of the track momentum at the PV, the corresponding ECAL cluster energy, and the energy sum of all bremsstrahlung photons associated with the track. The energy of muons is obtained from the corresponding track momentum. The energy of charged hadrons is determined from a combination of the track momentum and the corresponding ECAL and HCAL energies, corrected for the response function of the calorimeters to hadronic showers. Finally, the energy of neutral hadrons is obtained from the corresponding corrected ECAL and HCAL energies.

The electron momentum is estimated by combining the energy measurement in the ECAL with the momentum measurement in the tracker. The momentum resolution for electrons with pT≈45GeV from Z→ee decays ranges from 1.6 to 5.0%. It is generally better in the barrel region than in the endcaps, and also depends on the bremsstrahlung energy emitted by the electron as it traverses the material in front of the ECAL [40, 41]. Matching muons to tracks measured in the silicon tracker results in a pT resolution of 1% in the barrel and 3% in the endcaps for muons with pT up to 100GeV [42].

For each event, hadronic jets are clustered from these reconstructed particles using the infrared- and collinear-safe anti-kT algorithm [43, 44] with a distance parameter of 0.4. The jet momentum is determined as the vector sum of all particle momenta in the jet, and is found from simulation to be, on average, within 5–10% of the true momentum over the entire pT spectrum and detector acceptance. Pileup interactions can contribute additional tracks and calorimetric energy depositions to the jet momentum. To mitigate this effect, charged particles identified as originating from pileup vertices are discarded, and an offset correction is applied to correct for remaining contributions from neutral particles. Jet energy corrections are derived from simulation to bring the measured response of jets to that of particle level jets on average. In situ measurements of the momentum balance in dijet, photon+jet, Z+jet, and multijet events are used to account for any residual differences in the jet energy scale (JES) between data and simulation [45]. The jet energy resolution (JER) amounts typically to 15–20% at 30GeV, 10% at 100GeV, and 5% at 1TeV. Additional selection criteria are applied to each jet to remove jets potentially dominated by anomalous contributions from various subdetector components or reconstruction failures.

The missing transverse momentum vector p→Tmiss is the projection on the plane perpendicular to the beams of the negative vector momenta sum of all particles that are reconstructed with the particle-flow algorithm. The p→Tmiss is modified to account for corrections to the energy scale of the reconstructed jets in the event. The missing transverse momentum, pTmiss, is defined as the magnitude of the p→Tmiss vector, and it is a measure of the transverse momentum of particles leaving the detector undetected [46].

The trigger, reconstruction, and selection efficiencies are corrected in simulations to match those observed in the data. Lepton efficiencies (ϵℓ) are evaluated with data samples of dilepton events in the Z boson mass peak with the tag-and-probe method [47], and correction factors ϵℓdata/ϵℓMC, binned in pTℓ and ηℓ of the leptons, are implemented.

Event selection

Events with a high-pT lepton from the decay of a W boson are selected online by a trigger algorithm that requires the presence of an electron (muon) candidate with minimum pT of 27, 32, and 32 GeV (24, 27, and 24 GeV) during the 2016, 2017, and 2018 data-taking periods, respectively. Electrons and muons are selected using tight identification criteria following the reconstruction algorithms discussed in Refs. [40, 42]. The analysis follows the selection strategy used in Ref. [8] and requires the presence of a high-pT isolated lepton in the region |ηℓ|<2.4 and pTℓ>35GeV.

The combined isolation variable, Icomb, quantifies additional hadronic activity around the selected leptons. It is defined as the sum of the transverse momenta of neutral hadrons, photons, and charged hadrons in a cone with ΔR=(Δη)2+(Δϕ)2<0.3 (0.4) around the electron (muon) candidate, excluding the contribution from the lepton itself, where ϕ is the azimuthal angle in radians. Only charged particles originating from the PV are included in the sum to minimize the contribution from pileup interactions. The contribution of neutral particles from pileup vertices is estimated and subtracted from Icomb. For electrons, this contribution is evaluated with the jet area method described in Ref. [48]; for muons, it is assumed to be half the pT sum of all charged particles in the cone originating from pileup vertices. The factor one-half accounts for the expected ratio of neutral to charged particle production in hadronic interactions. The lepton candidate is considered to be isolated if Icomb/pTℓ<0.15. Events with an additional isolated lepton with pTℓ>20GeV are rejected to suppress the contribution from Z+jets and tt¯ events.

The transverse mass (mT) of the lepton and p→Tmiss is defined as,mT≡2pTℓpTmiss[1-cos(ϕℓ-ϕpTmiss)],

where ϕℓ and ϕpTmiss are the azimuthal angles of the lepton and the p→Tmiss vector. Events with mT<55GeV are discarded from the analysis to suppress the contamination from events composed uniquely of jets produced through the strong interaction, referred to as QCD multijet events. The contribution of this background was evaluated with two methods: (i) using a QCD multijet simulation; and (ii) by means of data control regions, inverting the selection requirements in transverse mass and lepton isolation to infer the contribution in the signal region. The contamination after OS-SS subtraction is negligible.

In addition to the requirements that select events with a W boson, we require the presence of at least one jet with pTjet>30GeV and |ηjet|<2.4. Jets with an angular separation between the jet axis and the selected isolated lepton ΔR(jet,ℓ)<0.4 are not considered.

Identification of charm jets 

Hadrons with b  and c  quark content decay through the weak interaction with lifetimes of the order of 10-12s and mean decay lengths larger than 100 μm at the energies relevant for this analysis. Secondary vertices well separated from the PV can be identified and reconstructed from the charged particle tracks. In a sizeable fraction of the heavy-flavor hadron decays (≈10–15% [36]) there is a muon in the final state. We make use of these properties to define two independent data samples enriched with jets originating from a c  quark: (i) the semileptonic (SL) channel, where a muon coming from the semileptonic decay of a c  hadron is identified inside a jet; and (ii) the secondary vertex (SV) channel, where a displaced SV is reconstructed inside a jet. The charge of the c  quark is determined from the charge of the muon in the SL channel, and the charges of the SV tracks in the SV case, as described in more detail below.

If an event fulfills both the SL and SV selection requirements (about 6% of the selected events), it is assigned to the SL channel. Thus, the SL and SV channels are mutually exclusive, i.e., the samples selected in each channel are statistically independent.

These two signatures also feature weakly decaying b hadrons. Events from processes involving the associated production of W bosons and b quarks are abundantly selected in the two categories. The dominant background contribution stems from tt¯ production, where a pair of W bosons and two b jets are produced in the decays of the top quark-antiquark pair. This final state mimics the analysis topology when at least one of the W bosons decays leptonically and one of the b jets contains an identified muon or a reconstructed SV. However, this background is effectively suppressed by the OS-SS subtraction. A tt¯ event will be categorized as OS (SS) when the lepton from the W decay and the muon or SV from the b  quark are coming from the same (different) top quark. The probability of identifying a muon or an SV inside the b (or b¯) jet with opposite or same charge as the charge of the W candidate is expected to be the same, thus producing an equal amount of OS and SS events.

Top quark-antiquark events where one of the W bosons decays hadronically into a cs¯ (or c¯s) pair may result in additional event candidates if the SL or SV signature originates from the c  jet. This topology produces genuine OS events, which contribute to the remaining background contamination after OS-SS subtraction. Similarly, single top quark production also produces OS events, but at a lower level because of the smaller production cross section. These remaining background contributions after OS-SS subtraction are estimated with simulations and are subtracted in the cross section measurements.

The production of a W boson and a single bottom quark through the process qg→W+b, similar to the one sketched in Fig. 1, produces OS events, but it is heavily Cabibbo-suppressed and its contribution is negligible. The other source of a W boson and a b  quark is W+bb¯ events where the bb¯ pair originates from a gluon splitting mechanism. These events are also charge-symmetric, since it is equally likely to identify the b  jet with the same or opposite charge than that of the W boson. This contribution also cancels out after the OS-SS subtraction. The same argument applies to W+cc¯ events.

Event selection in the SL channel

The W+c events with a semileptonic c  quark decay are selected by requiring a reconstructed muon among the constituents of any of the selected jets. Semileptonic c  quark decays into electrons are not considered because of a high background in identifying electrons inside jets. The muon candidate must satisfy the same reconstruction and identification quality criteria as those imposed on the muons from the W boson decay, except for isolation, and must be reconstructed in the region |η|<2.4, with pTμ<25GeV and pTμ/pTjet<0.6. The pT requirements reduce the contamination from prompt muons overlapping with or misreconstructed as jets. No minimum pT threshold is explicitly required, but the muon reconstruction algorithm sets a natural threshold of around 3 (2)GeV in the barrel (endcap) region since the muon must traverse the material in front of the muon detector and penetrate deep enough into the muon system to be reconstructed and satisfy the identification criteria. If more than one such muon is identified, the one with the highest pT is selected.

Additional requirements are applied for the event selection in the W→μν channel, since the selected sample is affected by a sizeable contamination from dimuon Z+jets events, where one of the muons from the Z decay is reconstructed inside a jet. The track of the muon coming from a semileptonic decay of a charm hadron tends to have a considerable transverse impact parameter with respect to the PV. We require the transverse impact parameter significance (IPS) of the muon in the jet, defined as the muon transverse impact parameter divided by its uncertainty, to be larger than 2. In addition, events with a dimuon invariant mass close to the Z boson mass peak (70<mμμ<110GeV) are discarded. Furthermore, mμμ must be larger than 12GeV to suppress the background from low-mass resonances.

The normalizations of the tt¯ and Z+jets backgrounds are derived from data control samples. A Z+jets data control sample is defined using the same selection criteria as the analysis but inverting the mμμ requirement to select events close to the Z boson mass peak (70<mμμ<110GeV). A normalization factor of 1.08±0.01 is required to match the Z+jets simulation with data. The tt¯ data control sample is established by selecting events with the same requirements as the analysis and additionally demanding at least three high-pT jets, two of which are tagged as b jets (using the loose working point of the DeepCSV b-tagging algorithm [49]), and the remaining jet contains a muon. A normalization factor of 0.92±0.02 is required to bring into agreement data and tt¯ simulation. The uncertainty in the background normalization factors reflects the statistical uncertainty of the data and the simulations in the control samples. Once the absolute normalization of the Z+jets and tt¯ backgroundTable 1 Data and background event yields (with statistical uncertainties) after selection and OS-SS subtraction for the SL channels (electron and muon W decay modes)

SL channel	Data	Background	
W→eν	424 047 ± 1286	80 646 ± 933	
W→μν	263 669 ±   918	68 108 ± 917	

Table 2 Simulated signal and background composition (in percentage) of the SL sample after selection and OS-SS subtraction. The W+QQ¯ stands for the sum of the contributions of W+cc¯ and W+bb¯

SL channel	W+c	W+QQ¯	W+udsg	Z+jets	tt¯	Single t	VV	
W→eν	81.0 ± 0.6	0.5 ± 0.3	3.1 ± 0.5	0.4 ± 0.1	10.0 ± 0.1	4.4 ± 0.1	0.6 ± 0.1	
W→μν	74.2 ± 0.5	0.5 ± 0.3	2.0 ± 0.4	5.5 ± 0.2	11.6 ± 0.1	5.8 ± 0.1	0.4 ± 0.1	

contributions are determined, the W+jets simulation is scaled so that the sum of the events from all predicted contributions be equal to the number of events in the selected data sample. The normalization factor of the W+jets simulation (0.95) has only a minor effect in the contribution of the (small) predicted W+udsg background. The overall normalization of the W+c signal simulation is irrelevant for the analysis, since it is only used for acceptance and efficiency calculations.

Events are classified as OS or SS depending on the electric charges of the lepton from the W boson decay and the muon inside the jet.

Table 1 shows the event yields in the W→eν and W→μν channels after the selection requirements described above and after OS-SS subtraction. The W→μν channel has a significantly lower yield due to the additional requirements to reduce the sizeable Z+jets background. The background yields, as estimated with the simulations, are also included in the table. The signal and background composition of the selected sample according to simulation is shown in Table 2. The fraction of signal W+c events in the W→eν channel is above 80%, whereas in the W→μν channel it drops to 74% because of the additional Z+jets background (around 6%). The dominant background, tt¯ production, where one of the W bosons decays leptonically and the other hadronically with a charm quark in the final state, amounts to approximately 10%.

Figure 2 shows the pT distributions of the muon inside the jet (upper) and of the lepton from the W decay (lower), for events in the selected SL sample, after the background normalization corrections described above. The simulations agree with the data within uncertainties.

Event selection in the SV channel

An independent W+c sample is selected by looking for secondary decay vertices of charmed hadrons within the reconstructed jets. Displaced SVs are reconstructed with either the simple secondary vertex (SSV) [50] or the inclusive vertex finder (IVF) [51, 52] algorithms. Both algorithms follow the adaptive vertex fitter technique [53] to construct an SV, but differ in the track selection used. The SSV algorithm takes as input the tracks constituting the jet, whereas the IVF algorithm starts from a displaced track with respect to the PV (seed track) and tries to build a vertex from nearby tracks in terms of their separation distance in three dimensions and their angular separation around the seed track. The IVF vertices are then associated to the closest jet in a cone of ΔR=0.3. Both SSV and IVF vertices always start with input tracks with a minimum pT of 1GeV to minimize the effects from poorly reconstructed tracks. Vertices reconstructed with the IVF algorithm are considered first. If no IVF vertex is found, SSV vertices are searched for, thus providing additional event candidates (about 3%). If more than one SV is reconstructed within a jet, the one with the highest pT, computed from its associated tracks, is selected. If there are several jets with an SV, only the SV associated to the jet of highest pT is selected.

At least three tracks must be associated with an SV for it to be considered. This requirement largely reduces the contamination of jets coming from the hadronization of light-flavor quarks (u, d, and s) or gluons. It also reduces the systematic uncertainty associated with the SV reconstruction efficiency. To ensure that the SV is well separated from the PV, we require the displacement significance, defined as the three dimensional distance between the PV and SV, divided by its uncertainty, to be larger than 8. This requirement suppresses the W+udsg background contribution below 1%.Fig. 2 Distributions after OS-SS subtraction of the pT of the muon inside the c jet (upper) and the pT of the lepton from the W decay (lower) for events in the SL sample, summing up the contributions of the W boson decay channels to electrons and muons. The contributions of the various processes are estimated with the simulated samples. The statistical uncertainty in the data is smaller than the size of the data dots. The hatched areas represent the sum in quadrature of statistical and systematic uncertainties in the MC simulation. The ratio of data to simulation is shown in the lower panels. The uncertainty band in the ratio includes the statistical uncertainty in the data, and the statistical and systematic uncertainties in the MC simulation

To classify the event as OS or SS, we measure the sign of the charge of the charm quark produced in the hard interaction. For charged charm hadrons, the sum of the charges of the decay products reflects the charge of the c  quark. For neutral charm hadrons, the charge of the closest hadron produced in the fragmentation process can indicate the charge of the c  quark [54, 55]. Hence, we assign a charge equal to the sum of the charges of the particle tracks associated with the SV. If the SV charge is zero, we assume the charge of the track that is closest in angular separation to the SV. We only consider PV tracks with pT>0.3GeV and within an angular separation from the SV direction of 0.1 in the (η,ϕ) space. If nonzero charge cannot be assigned, the event is rejected. According to the simulation, the charge assignment procedure provides a nonzero charge for 99% of the selected SVs, and the sign of the charge is correctly assigned in 83% of the cases.

The modeling of the SV charge assignment in the simulation has been validated with data. Events passing both the SL and SV selection criteria are used to compare the charges of the muon inside the jet and the SV. In 95% of these events the charges agree. The difference in the charge assignment efficiency between data and simulation, around 1%, is taken as a systematic uncertainty in the cross section measurements, as detailed in Sect. 6.

The SV reconstruction efficiency in the simulation is calibrated using data. The events of the SL sample are used to compute data-to-simulation scale factors for the efficiency of charm identification through the reconstruction of an SV [5, 49]. The fraction of events in the SL sample with an SV is computed for data and simulation, and the ratio of data to simulation is applied as a scale factor to the simulated W+c signal events in the SV sample. The calculated scale factor is 0.93±0.03, where the uncertainty accounts for statistical and systematic effects. The systematic uncertainty includes contributions from uncertainties in the pileup description, JES and JER, lepton efficiencies, background subtraction, and modeling of charm production and decay fractions in the simulation.

Table 3 shows the event yields in the W→eν and W→μν channels after the selection requirements and OS-SS subtraction. The background yields, as estimated with the simulations, are also included. The contributions of the backgrounds were rescaled using the normalization factors described in Sect. 5.1.1. The signal and background composition of the selected sample, as predicted by the simulation, are shown in Table 4. The purity of signal W+c events is above 80%. The dominant backgrounds come from tt¯ (8%) and single top (9%) production.Table 3 Data and background event yields (with statistical uncertainties) after selection and OS-SS subtraction for the SV channels (electron and muon W decay modes)

SV channel	Data	Background	
W→eν	338 504 ± 1717	60 565 ± 1577	
W→μν	494 264 ± 1876	94 356 ± 2002	

Table 4 Simulated signal and background composition (in percentage) of the SV sample after selection and OS-SS subtraction. The W+QQ¯ stands for the sum of the contributions of W+cc¯ and W+bb¯

SV channel	W+c	W+QQ¯	W+udsg	Z+jets	tt¯	Single t	VV	
W→eν	82.1 ± 0.8	0.7 ± 0.4	1.0 ± 0.6	0.1 ± 0.2	7.2 ± 0.1	8.4 ± 0.1	0.5 ± 0.1	
W→μν	80.9 ± 0.6	0.7 ± 0.3	0.5 ± 0.4	0.5 ± 0.2	8.0 ± 0.1	8.9 ± 0.1	0.5 ± 0.1	

The event selection requirements are summarized in Table 5 for the four selection channels of the analysis, the W boson decay channels to both electrons or muons, and the SL and SV charm identification channels.Table 5 Summary of the selection requirements for the four selection channels of the analysis

Figure 3 shows the distributions, after OS-SS subtraction, of the corrected SV mass and the SV transverse momentum divided by the jet transverse momentum, pTSV/pTjet. The latter is a representative observable of the energy fraction of the charm quark carried by the charm hadron in the fragmentation process. We define the corrected SV mass, mSVcorr, as the invariant mass of all charged particles associated with the SV, assumed to be pions, mSV, corrected for additional particles, either charged or neutral, that may have been produced but were not reconstructed [56]:mSVcorr=mSV2+pSV2sin2θ+pSVsinθ,

where pSV is the modulus of the vectorial sum of the momenta of all charged particles associated with the SV, and θ is the angle between the momentum vector sum and the vector from the PV to the SV. The corrected SV mass is thus the minimum mass the long-lived hadron can have that is consistent with the direction of its momentum.

The normalization of the single top quark background is fixed with data. Single top quark events populate the tail of the mSVcorr distribution. A normalization factor of 1.5±0.2 for the single top quark contribution was required to match data and simulation predictions. The same rescaling is applied to the SL and SV samples.Fig. 3 Distributions after OS-SS subtraction of the corrected SV mass (upper) and SV transverse momentum divided by the jet transverse momentum (lower) for events in the SV sample, summing up the contributions of the W boson decay channels to electrons and muons. The contributions from all processes are estimated with the simulated samples. The statistical uncertainty in the data is smaller than the size of the data dots for most of the data points. The hatched areas represent the sum in quadrature of statistical and systematic uncertainties in the MC simulation. The ratio of data to simulation is shown in the lower panels. The uncertainty band in the ratio includes the statistical uncertainty in the data, and the statistical and systematic uncertainties in the MC simulation

Systematic uncertainties

The impact of various sources of uncertainty in the measurements presented in Sect. 7 is estimated by recalculating the cross sections with the relevant parameters varied up and down by one standard deviation of their uncertainties.

The combined uncertainty in the trigger, reconstruction, and identification efficiencies for isolated leptons results in an uncertainty in the cross section measurements of about 2% (1%) for the W→eν (W→μν) channel. The uncertainty in the identification efficiency of nonisolated muons inside jets is approximately 3%, according to dedicated studies with Z+jets events. This uncertainty affects only the SL channel.

The effects of the uncertainty in the JES and JER are assessed by varying up and down the pT values of jets with the corresponding uncertainty factors. The JES and JER uncertainties are also propagated to p→Tmiss. The resulting uncertainty in the cross section is about 2% (1%) for the SL (SV) channel. The uncertainty from a p→Tmiss mismeasurement in the event is estimated by varying within its uncertainty the contribution of the energy unassociated with reconstructed particle-flow objects. The effect in the cross section measurement is <0.5%. Uncertainties in the pileup modeling are calculated using a modified pileup profile obtained by changing the mean number of interactions by ≈5%. This variation covers the uncertainty in the pp inelastic cross section [57] and in the modeling of the pileup simulation. It results in less than 0.5% uncertainty in the cross section measurements.

The integrated luminosities of the 2016, 2017, and 2018 data-taking periods are individually known with uncertainties in the 1.2–2.5% range [58–60], whereas the total 2016–2018 integrated luminosity has an uncertainty of 1.6%. The improvement in precision arises from the (uncorrelated) time evolution of some systematic effects.

The uncertainty in the scale factor correcting the SV reconstruction efficiency in the simulation propagates into a systematic uncertainty of 3% in the cross section. The uncertainty in the SV charge determination is estimated as the difference (1%) in the rate obtained in data and simulation of correct SV charge assignment in the validation test described in Sect. 5.1.2.

Because of the dependence of the SV reconstruction efficiency on the SV displacement, we have evaluated the effect produced by an imperfect modeling of this observable by reweighting the SV displacement significance distribution of the simulation to match that of the data. The resulting uncertainty in the cross section measurement is 1–2%. In addition, the stability of the results with the minimum SV displacement significance requirement was checked by changing the threshold from 8 to 7. The effect in the results is also at the 1% level.

The background contributions are evaluated with the simulations validated in data control samples, as discussed in Sect. 5.1.1. The uncertainty in the predicted background levels has an effect of 1% in the cross section measurements.

The signal samples used for the acceptance and efficiency calculations were generated with MadGraph+ pythia8 using the NNPDF3.0 and NNPDF3.1 PDF sets. The envelope of the systematic variations (replicas) of the nominal PDF is assumed to be the systematic uncertainty due to an imperfect knowledge of the PDFs, as recommended in Ref. [61]. The effect is approximately 1%. The statistical uncertainty in the determination of the selection efficiency using the simulated samples is 1%, and is propagated as an additional systematic uncertainty.

In the signal and background modeling, no uncertainty is included in the simulation of higher-order terms in perturbative QCD (parton shower). The OS-SS subtraction technique removes the contribution to W+c production coming from charm quark-antiquark pair production, rendering the measurement insensitive to this effect. The uncertainty in the modeling of the hard process in the signal simulation is assessed by independently changing the QCD factorization and renormalization scales by factors of 0.5 and 2 relative to the nominal value. The resulting uncertainty in the cross section measurement is negligible.

To estimate the effect produced by the uncertainties in the corrected values used in the simulation for the charm fragmentation and decay branching fractions [35, 36], we have varied those values within their uncertainties. The impact in the cross section measurements is 1–2%, both for the fragmentation and decay branching fractions.

The main systematic uncertainties are summarized in Table 6 for the four selection channels of the analysis. Overall, the total systematic uncertainty in the W+c fiducial cross section is approximately 5% in all channels.Table 6 Summary of the main systematic uncertainties, in percentage of the measured fiducial cross section, for the four selection channels of the analysis

	SL	SL	SV	SV	
	W→eν	W→μν	W→eν	W→μν	
Source	Uncertainty [%]	
Isolated lepton identification	1.6	0.9	1.6	0.9	
Jet energy scale and resolution	2.0	2.0	1.0	1.0	
Muon in jet identification	3.0	3.0	–	–	
SV reconstruction	–	–	3.7	3.7	
Charm fragmentation and decay	2.6	2.6	2.4	2.4	
PDF in MC samples	1.0	1.0	1.0	1.0	
Stat. uncert. selection efficiency	0.9	1.2	0.9	0.8	
Background contributions	0.6	0.9	1.3	1.3	
Integrated luminosity	1.6	1.6	1.6	1.6	
Total	5.2	5.1	5.4	5.2	

Cross section measurements

The W+c production cross section measurements are restricted to a phase space region that is close to the experimental fiducial volume with optimized sensitivity for the signal process. Cross sections are measured inclusively within the fiducial phase space region and differentially as a function of pTℓ and |ηℓ|. Cross section measurements are performed independently in four different channels, the two charm identification SL and SV channels, and the two W boson decay channels. The four measurements are combined to improve the precision.

Measurements are unfolded to the particle and parton levels. At both levels, the fiducial region is defined by a lepton at the generator level coming from the decay of a W boson with pTℓ>35GeV and |ηℓ|<2.4, together with a generator-level c  jet with pTc jet>30GeV and |ηc jet|<2.4. The OS-SS subtraction is also applied at generator level. This removes the charge-symmetric contributions that mostly originate from gluon splitting into a charm quark-antiquark pair. The c  jet must be well separated from the lepton by an angular distance ΔR(c jet,ℓ)>0.4. Jets at the generator level are clustered using the anti-kT jet algorithm with a distance parameter R=0.4. At the particle level, jets are formed using generator particles produced after the hadronization process. At the parton level, jets are constructed from the hard interaction partons.

For all channels under study, the W+c cross section is determined using the following expression:1 σ(W+c)=Ysel-YbkgCL,

where Ysel is the selected OS-SS event yield, and Ybkg the background yield in data after OS-SS subtraction, estimated from simulation and normalized using the data control samples described in Sect. 5.1. L is the integrated luminosity of the data sample.

The factor C corrects for acceptance and efficiency losses in the selection process of W+c events produced in the fiducial region at the generator level. It also subtracts the contributions from W+c events outside the kinematic region of the measurements and from W+c events with W→τν, τ→e+X or τ→μ+X. It is calculated, using the sample of simulated signal events, as the ratio between the event yield of the selected W+c sample (according to the procedure described in Sects. 5.1.1 and 5.1.2 and after OS-SS subtraction) and the number of OS-SS W+c events satisfying the phase space definition at the generator level. Independent correction factors C are computed at the particle and parton levels, and for the four selection channels.

Measurements at the particle level

Cross section measurements, unfolded to the particle level, are presented in this section. The fiducial W+c production cross section measurements computed with Eq. (1) for the four channels separately are shown in Table 7, together with the event yields and the C correction factors. The different C values reflect the different reconstruction and selection efficiencies in the four channels. In the SL channel, less than 5% of the signal charm hadrons generated in the fiducial region of the analysis produce a muon in their decay with enough momentum to reach the muon detector and get reconstructed. Similarly, in the SV channel, less than 5% of the events with a charm hadron decay remain after SV reconstruction, SV charge assignment, and OS-SS subtraction. The remaining inefficiency, accounted for in the C correction factor, is due to the selection requirements of the samples.Table 7 Measured production cross sections σ(W+c) unfolded to the particle level in the four selection channels together with statistical (first) and systematic (second) uncertainties. The acceptance times efficiency values (C) are also given

Channel	C(%)	σ(W+c) [pb]	
W→eν, SL	1.568 ± 0.014 ± 0.077	158.7 ± 0.6 ± 8.3	
W→μν, SL	0.946 ± 0.011 ± 0.044	149.8 ± 0.7 ± 7.7	
W→eν, SV	1.389 ± 0.013 ± 0.068	145.0 ± 0.9 ± 7.6	
W→μν, SV	1.966 ± 0.015 ± 0.093	147.4 ± 0.7 ± 7.5	

Results obtained for the W+c cross sections in the four different channels are consistent within the uncertainties, and are combined using the best linear unbiased estimator method [62] that takes into account individual uncertainties and their correlations. Systematic uncertainties arising from a common source and affecting several measurements are considered as fully correlated. In particular, all systematic uncertainties are assumed fully correlated between the electron and muon channels, except those related to the lepton reconstruction. The χ2 of the combination is 4.8 (three degrees of freedom), corresponding to a p-value of 0.19. The combined measured cross section unfolded to the particle level is:σ(W+c)=148.7±0.4(stat)±5.6(syst)pb.

Measurements are compared with the predictions of the MadGraph5_amc@nlo MC generator, as shown in Fig. 4. In the predictions, two different NNPDF PDF sets (versions 3.0 and 3.1) are used. The two predictions differ as well in the tune used in pythia8 for the parton showering, hadronization, and underlying event modeling (CUETP8M1 and CP5). The predicted cross sections are about 10% (using NLO NNPDF3.0) and 20% (NNLO NNPDF3.1) higher than the measured value, with relative uncertainties close to 10%. The uncertainty associated with the MC predictions includes the uncertainties associated with the renormalization and factorization scales, as well as the uncertainty related to the PDFs used in the simulation. The scale uncertainties are estimated using a set of weights provided by the generator that corresponds to independent variations of the scales by factor of 0.5, 1, and 2. The prediction is obtained for all combinations (excluding the cases where one scale is reduced and the other is increased at the same time) and their envelope is quoted as the uncertainty. The uncertainty in the PDFs is estimated using different Hessian eigenvectors of each PDF set.Fig. 4 Comparison of the measured fiducial σ(W+c) cross section unfolded to the particle level with the predictions from the MadGraph5_amc@nlo simulation using two different PDF sets (NLO NNPDF3.0 and NNLO NNPDF3.1). Two different tunes (CUETP8M1 and CP5) for the parton showering, hadronization and underlying event modeling in pythia8 are also used. Horizontal error bars indicate the total uncertainty in the predictions

The σ(W+c) production cross section is also measured differentially as a function of |ηℓ| and pTℓ. The total sample is divided into subsamples according to the value of |ηℓ| or pTℓ, and the cross section is computed using Eq. (1). The binning of the differential distributions is chosen such that each bin is sufficiently populated to perform the measurement. Event migration between neighbouring bins caused by detector resolution effects is evaluated with the simulated signal sample and is negligible. Measurements in the four channels are combined assuming that systematic uncertainties are fully correlated among bins of the differential distributions.Fig. 5 Measured differential cross sections dσ(W+c)/d|ηℓ| (upper) and dσ(W+c)/dpTℓ (lower) unfolded to the particle level, compared with the predictions of the MadGraph5_amc@nlo simulation. Two different PDF sets (NLO NNPDF3.0 and NNLO NNPDF3.1) are used. Error bars on data points include statistical and systematic uncertainties. Symbols showing the theoretical expectations are slightly displaced in the horizontal axis for better visibility. The ratios of data to predictions are shown in the lower panels. The uncertainty in the ratio includes the uncertainties in both data and prediction

Table 8 Measured production cross sections σ(W+c) unfolded to the parton level in the four selection channels together with statistical (first) and systematic (second) uncertainties. The acceptance times efficiency values (C) are also given

Channel	C(%)	σ(W+c) [pb]	
W→eν, SL	1.419 ± 0.012 ± 0.069	175.3 ± 0.7 ± 9.2	
W→μν, SL	0.856 ± 0.010 ± 0.040	165.4 ± 0.8 ± 8.5	
W→eν, SV	1.261 ± 0.012 ± 0.062	159.6 ± 1.0 ± 8.4	
W→μν, SV	1.786 ± 0.014 ± 0.084	162.3 ± 0.8 ± 8.2	

Systematic uncertainties in the differential σ(W+c) cross section measurements are in the range of 4–6%. The main sources of systematic uncertainty, as discussed in Sect. 6, are related to the charm hadron fragmentation and decay fractions in the simulation (2%), and the efficiency of identifying an SV or a muon inside a jet (3%).

The σ(W+c) differential cross section as a function of |ηℓ| and pTℓ, obtained after the combination of the measurements in the SL, SV, electron, and muon channels, is shown in Fig. 5, compared with the predictions from the MadGraph5_amc@nlo simulation. Observed shape differences are within 10%.

Measurements at the parton level

The measurements are also unfolded to the parton level, including an additional correction to account for the c  quark fragmentation and hadronization processes. Results of the fiducial cross sections in the four selection channels are presented in Table 8. The combination of the measurements is:σ(W+c)=163.4±0.5(stat)±6.2(syst)pb.

The fiducial cross section measured at the parton level is expected to be slightly larger than that at the particle level. During the hadronization and jet clustering processes, the momentum of the c  quark gets smeared and biased towards slightly smaller values. A fraction of charm quarks near the pTc>30GeV threshold of the fiducial region of the measurement do not result in c  jets with pTc jet>30GeV. On the other hand, a number of W+c events with a c  quark with pTc<30GeV get reconstructed with a generator level jet with pTc jet>30GeV. The net effect is the the observed reduction of about 10% of the cross section at the particle level.

The measurements unfolded to the parton level are compared with analytical calculations of W+c production. We have used the MCFM 9.1 program [16] to evaluate the cross section predictions in the phase space of the analysis: pTℓ>35GeV, |ηℓ|<2.4, pTc jet>30GeV, and |ηc jet|<2.4. Jets are clustered in MCFM using the anti-kT jet algorithm with a distance parameter R=0.4. The W+c process description is available in MCFM up to O(αS2) with a massive charm quark (mc=1.5GeV). The contributions from gluon splitting into cc¯ are not included. We have computed predictions for the following NLO PDF sets: MSHT20 [63], CT18 [64], CT18Z [64], ABMP16 [65], NNPDF3.0 [29], and NNPDF3.1 [30]. The LHAPDF6 library [66] was used to access the PDF sets. All of the PDF sets were derived using strangeness-sensitive experimental data, including LHC W/Z  and jet production cross section measurements. The NNPDF and MSHT20 sets additionally incorporate the CMS W+c production at s=7TeV data. CTA18Z differs from CTA18 because the former includes the ATLAS W/Z  7TeV precision measurements [67] leading to an enhancement of the strange PDF. The PDF parameterizations of the MSHT20 and NNPDF groups allow for strangeness asymmetry.

The factorization and the renormalization scales are set to the value of the W boson mass [36]. The uncertainty from missing higher perturbative orders is estimated by computing cross section predictions varying independently the factorization and renormalization scales to twice and half their nominal values, with the constraint that the ratio of scales is never larger than 2. The envelope of the resulting cross sections with these scale variations defines the theoretical scale uncertainty. The value in the calculation of the strong coupling constant at the energy scale of the mass of the Z boson, αS(mZ), is set to the recommended values by each of the PDF groups. Uncertainties in the predicted cross sections associated with αS(mZ) are evaluated as half the difference in the predicted cross sections evaluated with a variation of Δ(αS)=±0.002.Table 9 Predictions for σ(W+c) production from MCFM at NLO in QCD for the phase space of the analysis. For every PDF set, the central value of the prediction is given, together with the uncertainty as prescribed from the PDF set, and the uncertainties associated with the scale variations and with the value of αS. The total uncertainty is given in the last column. The last row in the table gives the experimental result presented in this paper

PDF set	σ(W+c) [pb]	ΔPDF [pb]	Δscales [pb]	ΔαS [pb]	Total uncert. [pb]	
MSHT20	176.3	-6.3+6.8	-7.4+6.8	±0.01	-9.7+9.6	
CT18	164.9	-8.7+11.1	-6.8+6.1	-0.8+0.9	-11.1+12.7	
CT18Z	176.4	-10.5+13.5	-7.4+7.0	-0.5+0.6	-12.8+15.2	
ABMP16	183.6	±3.3	-7.8+7.2	-0.9+1.5	-8.4+7.9	
NNPDF3.0	161.9	±6.2	-6.7+5.8	±0.01	-9.1+8.5	
NNPDF3.1	175.2	±6.1	-7.3+6.6	±0.01	-9.5+9.1	
CMS: 163.4±0.5(stat)±6.2(syst)pb

The theoretical predictions for the fiducial W+c cross section in the phase space of the measurements are summarized in Table 9. The central value of the prediction is provided together with the relative uncertainties arising from the PDF variations within each set, the choice of scales, and αS. The size of the PDF uncertainties depends on the different input data and methodology used by the various groups. In particular, they depend on the parameterization of the strange quark PDF and on the definition of the one standard deviation uncertainty band. The maximum difference between the central values of the various PDF predictions is ∼10%. This difference is comparable to the total uncertainty in each of the individual predictions. Theoretical predictions are slightly larger than the measured cross section but are in agreement within the uncertainties, as depicted in Fig. 6.Fig. 6 Comparison of the experimental measurement of σ(W+c), unfolded to the parton level, with the predictions from the NLO QCD MCFM calculations using different NLO PDF sets. Horizontal error bars indicate the total uncertainty in the predictions

Fig. 7 Measured differential cross sections dσ(W+c)/d|ηℓ| (upper) and dσ(W+c)/dpTℓ (lower) unfolded to the parton level, compared with the predictions from the MCFM NLO calculations using different NLO PDF sets. Error bars on data points include statistical and systematic uncertainties. Symbols showing the theoretical expectations are slightly displaced in the horizontal axis for better visibility. The ratios of data to predictions are shown in the lower panels. The uncertainty in the ratio includes the uncertainties in both data and prediction

The predictions for the σ(W+c) production cross section, computed in intervals of |ηℓ| and pTℓ, are compared with the measured values in Fig. 7. The predictions are generally consistent with the measurements within uncertainties, except for the highest pTℓ bin.

Measurements of the cross section ratio σ(W++c¯)/σ(W-+c)

The cross section ratio σ(W++c¯)/σ(W-+c) is measured in the four channels as the ratio of the OS-SS event yields in which the lepton from the W boson decay is positively or negatively charged:2 Rc±=σ(W++c¯)σ(W-+c)=Ysel+-Ybkg+Ysel--Ybkg-.

The OS-SS background contributions, Ybkg+ and Ybkg-, estimated with the simulations, are subtracted from the selected event yields Ysel+ and Ysel-. The statistical uncertainty in the background contributions in the four analysis channels is treated as a source of systematic uncertainty (0.5-0.8%) in the cross section ratio.

Most of the reconstruction and selection efficiencies cancel out in the measurement of the cross section ratio Rc±. Possible efficiency differences between positive and negative leptons and SVs are included as systematic uncertainties. We evaluate effects stemming from charge confusion and charge-dependent reconstruction efficiencies.

The probability of assigning the incorrect charge to a lepton is studied with data using Z→ℓℓ events reconstructed with SS or OS leptons. For the muons, the charge misidentification probability is negligible (<10-3). For the electrons, the effect is around 1% but propagates into a negligible uncertainty in the cross section ratio. The charge confusion rate for the SVs is significantly larger, 17%, as described in Sect. 5.1.2. However, assuming that the charge confusion probability is the same for positive and negative SVs, the effect in the cross section ratio cancels out.

Potential differences in the reconstruction efficiencies of positive and negative leptons or SVs are studied with the W+c MC simulation. Efficiency ratios are calculated independently for the four channels of the analysis and are consistent with unity within the statistical uncertainty (1.2–1.4%). No corrections are made in the Rc± measurements but the statistical uncertainties in the efficiency ratios are treated as systematic uncertainties.Table 10 Measured production cross section ratio Rc± in the four selection channels. Statistical (first) and systematic (second) uncertainties are also given

Channel	Rc±	
W→eν, SL	0.934 ± 0.006 ± 0.013	
W→μν, SL	0.940 ± 0.006 ± 0.014	
W→eν, SV	0.961 ± 0.008 ± 0.013	
W→μν, SV	0.974 ± 0.006 ± 0.015	

Fig. 8 Comparison of the experimental measurement of Rc± with the NLO QCD MCFM calculations using different NLO PDF sets. Horizontal error bars indicate the total uncertainty in the predictions

The Rc± measurements in the four channels are presented in Table 10. The four measurements are combined considering as fully correlated the systematic uncertainties of electron, muon and SV reconstruction efficiencies affecting several channels. The χ2 of the combination is 3.3 (three degrees of freedom), corresponding to a p value of 0.35. The combined cross section ratio measurement is:Rc±=0.950±0.005(stat)±0.010(syst).

The precision in the Rc± measurement has been improved by a factor of two with respect to previous CMS measurements [7–9], leading to the most precise measurement of Rc± to date.

In Fig. 8 the Rc± measurement is compared with the MCFM calculations using various PDF sets. Theoretical predictions for σ(W++c¯) and σ(W-+c) are computed independently under the same conditions explained in Sect. 7.2 and for the same |ηℓ| and pTℓ ranges used in the analysis. Expectations for Rc± are derived from them and presented in Table 11. All theoretical uncertainties are significantly reduced in the cross section ratio prediction.Table 11 Theoretical predictions for Rc± calculated with MCFM at NLO. The kinematic selection follows the experimental requirements. For every PDF set, the central value of the prediction is given, together with the uncertainty as prescribed from the PDF set, and the uncertainties associated with the scale variations and with the value of αS. The total uncertainty is given in the last column. The last row in the table gives the experimental result presented in this paper

PDF set	Rc±	ΔPDF	Δscales	ΔαS	Total uncert.	
MSHT20	0.948	-0.011+0.021	±0.001	±0.0001	-0.011+0.021	
CT18	0.955	±0.003	±0.003	±0.001	±0.003	
CT18Z	0.958	±0.003	±0.001	±0.001	±0.003	
ABMP16	0.964	±0.002	±0.001	±0.001	±0.002	
NNPDF3.0	0.935	±0.017	±0.001	±0.0001	±0.017	
NNPDF3.1	0.939	±0.020	±0.001	±0.0001	±0.020	
CMS: 0.950±0.005(stat)±0.010(syst)

The Rc± observable is sensitive to a potential strangeness asymmetry in the proton but also to the down quark and antiquark asymmetry through the Cabibbo-suppressed down quark contribution to the W+c production. In the absence of strangeness asymmetry, as in the PDF sets CT18 and ABMP16, the predicted Rc± value in the kinematical region of the analysis ranges from 0.955 to 0.964 with a small uncertainty of about 0.2%. The predictions calculated using PDF sets that include strangeness asymmetry in the proton (MSHT20 and NNPDF) are about 2% lower, ranging from 0.935 to 0.948 with a 2% uncertainty as a result of the larger uncertainty associated with the difference between the strange quark and antiquark PDFs. Within experimental and theoretical uncertainties, the measured Rc± value is consistent with both sets of predictions.Fig. 9 Measured cross section ratio Rc± as a function of the absolute value of ηℓ (upper) and pTℓ (lower), compared with the NLO QCD MCFM calculations using different NLO PDF sets. Error bars on data points include statistical and systematic uncertainties. Symbols showing the theoretical expectations are slightly displaced in the horizontal axis for better visibility. The ratios of data to predictions are shown in the lower panels. The uncertainty in the ratio includes the uncertainties in both data and prediction

Table 12 Predictions for σ(W+c) in the phase space of the analysis. For each QCD and EW order, the central values of the OS, SS and OS-SS predictions are given, together with the statistical, scales, PDF, and total uncertainties of the OS-SS prediction. All values are given in pb. The last row in the table gives the experimental result presented in this paper

QCD order	EW order	σW+cOS	σW+cSS	σW+cOS-SS	ΔstatOS-SS	ΔscalesOS-SS	ΔPDFOS-SS	ΔTotalOS-SS	
LO	LO	137.4	0	137.4	±0.1	-13.3+16.6	±5.1	-14.3+17.4	
NLO	LO	182.4	4.1	178.3	±0.3	-9.4+9.3	±6.8	-11.6+11.6	
NNLO	LO	182.9	8.2	174.7	±1.0	-2.8+1.2	±6.8	-7.4+7.0	
NNLO	NLO	179.1	8.0	171.1	±1.0	-2.8+1.2	±6.8	-7.4+7.0	
CMS: 163.4±0.5(stat)±6.2(syst)pb

The cross section ratio Rc± is also measured differentially as a function of |ηℓ| and pTℓ. The measurements are compared with the MCFM predictions in Fig. 9. The predictions are generally consistent with the measurements, with some small deviations in shape within 5%. The cross section ratio decreases with |ηℓ| from Rc±∼1 in the central region to about 0.87 for the most forward lepton pseudorapidity values. This behaviour is expected since different Bjorken x regions are being probed. At larger x values, corresponding to higher values of |ηℓ|, W-+c production increases relative to W++c¯ because of the growing contribution initiated by the valence down quark. The differences between the predictions made using PDF sets with and without strange quark asymmetry grow with increasing |ηℓ| and pTℓ. However, with the current uncertainties, the data cannot distinguish between both sets of predictions.

Comparison with predictions using NNLO QCD and NLO EW calculations

The first computation of NNLO QCD corrections for W+c production has recently been presented [14, 15]. The latest calculations include full off-diagonal CKM dependence up to NNLO QCD accuracy, and the dominant NLO EW corrections. In addition, a modified anti-kT jet algorithm (flavored anti-kT [68]) is used to guarantee that the computations are infrared safe. This is important for a fair comparison between theory predictions and experimental measurements, since experimental results are derived using the anti-kT jet algorithm.

Predictions corresponding to the phase space of the CMS measurements presented in this paper, pTℓ>35GeV, |ηℓ|<2.4, pTc jet>30GeV, |ηc jet|<2.4, ΔR(jet,ℓ)>0.4, have been specifically computed for the purpose of this comparison, using the charge-dependent flavored anti-kT jet algorithm with parameter a=0.1, and the same input parameters as in Ref. [15]. The theoretical cross sections are provided at LO, NLO, and NNLO QCD accuracies. At LO, the W+c process is defined at order O(αSα2) in the strong and EW couplings. At NLO, the QCD corrections include all virtual and real contributions of order O(αS2α2). In the same way, at NNLO accuracy all double-virtual, double-real, and real-virtual contributions of order O(αS3α2) are included. The calculation is carried out in the 5-flavor scheme with massless bottom and charm quarks. NLO EW corrections of order O(αSα3) are calculated including all virtual corrections and the real corrections involving single real photon emission to cancel the corresponding IR divergences appearing in the EW one-loop amplitude.Fig. 10 Comparison of the experimental measurement of σ(W+c) with the OS-SS LO, NLO, and NNLO QCD predictions, and NLO EW corrections. The NNLO QCD NNPDF3.1 PDF set is used for computing all the predictions. CMPP stands for the authors of the calculations [15]. Horizontal error bars indicate the total uncertainty in the predictions

Fig. 11 Comparison of the measured differential cross sections dσ(W+c)/d|ηℓ| (upper) and dσ(W+c)/dpTℓ (lower) with the OS-SS LO, NLO, and NNLO QCD predictions, and NLO EW corrections. The NNLO QCD NNPDF3.1 PDF set is used for computing all the predictions. CMPP stands for the authors of the calculations [15]. Error bars on data points include statistical and systematic uncertainties. Symbols showing the theoretical expectations are slightly displaced in the horizontal axis for better visibility. The ratios of data to predictions are shown in the lower panels. The uncertainty in the ratio includes the uncertainties in both data and prediction

The nominal renormalization and factorization scales are set both to 12(ET,W+pTc jet), where ET,W=MW2+(p→Tℓ+p→Tν)2. To estimate missing higher-order QCD corrections, the scale uncertainty is obtained by independently varying the two scales by factors of 0.5, 1, 2, and taking the envelope of the predictions obtained with all variations excluding the cases where one scale is reduced and the other is increased at the same time.

The calculation was performed for the most representative PDF set, which allows for strange asymmetry, NNPDF3.1. The NNLO QCD PDF set was used for computing the predictions for all orders, following the PDF4LHC recommendation [61]. To evaluate the PDF uncertainty of the NNPDF3.1 sets, specialized minimal PDF sets [69], which contain only 8 replicas, were used. The PDF uncertainty is calculated as the square root of the quadratic sum of the differences between the cross section obtained with the nominal PDF and that obtained with each replica.

In Table 12, the theoretical predictions for the OS, SS, and OS-SS inclusive fiducial cross section are given at LO, NLO, and NNLO QCD accuracies. The QCD corrections show good perturbative convergence, since the NNLO QCD corrections are significantly smaller than the NLO ones. The NNLO correction for the OS-SS cross section is negative, about - 2%. This occurs becausse the NNLO QCD corrections to SS are larger than those for OS; at LO there is no SS contribution to the W+c process and the first SS contribution enters at NLO. The cross section calculated at NNLO QCD including NLO EW corrections is also shown in Table 12. The EW corrections amount to -2%. They were included as a multiplicative factor with negligible statistical uncertainty.

At LO and NLO the total uncertainty in the predictions is dominated by the scale uncertainty (around 5% at NLO). At NNLO the scale uncertainty is reduced to 1%, and the PDF uncertainty (4%) dominates. The inclusion of NNLO QCD corrections provides a more precise determination of the strange quark content of the proton from the cross section observable.

The OS-SS predictions are compared with the fiducial cross section measurement in Fig. 10. The OS-SS subtraction reduces the NNLO corrections, but does not remove them completely. The inclusion of the NNLO corrections decreases the uncertainty in the prediction and also brings it closer to the experimental measurement. The EW NLO corrections further improves the agreement between the theoretical prediction and experimental data. The theoretical prediction and the experimental measurement agree within uncertainties.

No efficiency correction has been applied to account for the different flavor assignments in the jet algorithms of the predictions (flavored anti-kT) and the experimental measurements (anti-kT). In Ref. [15] the difference in the predictions from the standard anti-kT and the flavored anti-kT algorithms is studied. Due to the lack of flavored infrared safety for the standard anti-kT algorithm, such a comparison can be done only at NLO with the help of a parton shower. The difference in the fiducial cross section predictions is below 1%. Similarly, the effect in the NNLO theoretical W+c cross section prediction using variations of the flavored anti-kT algorithm, and the flavored kT algorithm is studied. Differences are also below 1%.Table 13 Theoretical predictions for Rc±. For each QCD order, the central values are given, together with the MC statistical, scales, PDF, and total uncertainties. The last row in the table gives the experimental result presented in this paper

QCD order	Rc±	Δstat	Δscales	ΔPDF	ΔTotal	
LO	0.945	±0.001	±0.001	±0.022	±0.022	
NLO	0.939	±0.004	±0.002	±0.023	±0.023	
NNLO	0.936	±0.011	±0.002	±0.023	±0.026	
CMS: 0.950±0.005(stat)±0.010(syst)

Fig. 12 Comparison of the experimental measurement of Rc± with the OS-SS LO, NLO and NNLO QCD predictions. The NNLO QCD NNPDF3.1 PDF set is used for computing all the predictions. CMPP stands for the authors of the calculations [15]. Horizontal error bars indicate the total uncertainty in the predictions

The predictions are also compared with the differential cross section measurements dσ(W+c)/d|ηℓ| and dσ(W+c)/dpTℓ in Fig. 11. The NLO correction is approximately flat in |ηℓ| while it is larger at low and high values of pTℓ. The NLO predictions are very similar to those shown in Fig. 7 calculated with MCFM at NLO using the same PDF set (NNPDF3.1). The NNLO correction is small and does not change the shape of the NLO predictions. The EW NLO correction is flat in |ηℓ| and gets larger with pTℓ, from 0.99 in the first bin to 0.90 in the highest pTℓ bin.

Predictions for the OS-SS cross section ratio Rc± have also been computed and are collected in Table 13. In computing the scale variation of Rc±, the scale uncertainty for the positive and negative signatures is taken as correlated. The Rc± observable is rather stable under perturbative QCD corrections, varying by less than 1% from LO to NNLO accuracy. The NLO EW correction does not affect Rc±, the change being smaller than 0.1%.

The comparison of the predictions with the fiducial inclusive and differential measurements are presented in Figs. 12 and 13. The inclusion of the NNLO QCD correction does not change the good agreement already observed with the predictions at NLO.Fig. 13 Comparison of the measured differential cross section ratio Rc± as a function of the absolute value of ηℓ (upper) and pTℓ (lower) with the OS-SS LO, NLO, and NNLO QCD predictions. The NNLO QCD NNPDF3.1 PDF set is used for computing all the predictions. CMPP stands for the authors of the calculations [15]. Error bars on data points include statistical and systematic uncertainties. Symbols showing the theoretical expectations are slightly displaced in the horizontal axis for better visibility. The ratios of data to predictions are shown in the lower panels. The uncertainty in the ratio includes the uncertainties in the data and prediction

Summary

The associated production of a W boson with a charm quark (W+c) in proton–proton (pp) collisions at a center-of-mass energy of 13TeV was studied with a data sample collected by the CMS experiment corresponding to an integrated luminosity of 138fb-1. The W+c process is selected based on the presence of a high transverse momentum lepton (electron or muon), coming from a W boson decay, and a jet with the signature of a charm hadron decay. Charm hadron decays are identified either by the presence of a muon inside a jet or by reconstructing a secondary decay vertex within the jet. Measurements are combined from the four different channels: electron and muon W boson decay channels, muon and secondary vertex charm identification channels.

Cross section measurements, within a fiducial region defined by the kinematics of the lepton from the W boson decay and the jet originated by the charm quark (pTℓ>35GeV, |ηℓ|<2.4, pTc jet>30GeV, |ηc jet|<2.4), are unfolded to the particle and parton levels. Cross sections are also measured differentially, as functions of |ηℓ| and pTℓ. The cross section ratio for the processes W++c¯ and W-+c is measured as well, achieving the highest precision in this measurement to date.

The measured fiducial σ(W+c) production cross section unfolded to the particle level is:σ(pp→W+c)B(W→ℓν)=148.7±0.4(stat)±5.6(syst)pb.

The cross section measurement unfolded to the parton level yields:σ(pp→W+c)B(W→ℓν)=163.4±0.5(stat)±6.2(syst)pb.

The measured σ(W++c¯)/σ(W-+c) cross section ratio is:σ(pp→W++c¯)σ(pp→W-+c)=0.950±0.005(stat)±0.010(syst).

The measurements are compared with theoretical predictions. The particle level measurements are compared with the predictions of the MadGraph5_amc@nlo MC generator. The parton level cross section measurements are compared with NLO QCD calculations from the MCFM program using different PDF sets and with recently available NNLO QCD calculations including NLO EW corrections. The predicted fiducial cross section and cross section ratio are consistent with the measurements within uncertainties. The NNLO QCD and NLO EW corrections improve the agreement between the predicted and measured cross sections. Despite the improvement in precision of the cross section ratio measurement compared with previous studies, discrimination between predictions using symmetric or asymmetric strange quark and antiquark PDFs would require a further reduction of experimental and theoretical uncertainties. The theoretical uncertainty is dominated by the PDF uncertainties. The inclusion of the cross section measurements in future PDF fits should improve the modeling of the strange parton distribution function of the proton.

Acknowledgements

We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid and other centers for delivering so effectively the computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construction and operation of the LHC, the CMS detector, and the supporting computing infrastructure provided by the following funding agencies: SC (Armenia), BMBWF and FWF (Austria); FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, FAPERGS, and FAPESP (Brazil); MES and BNSF (Bulgaria); CERN; CAS, MoST, and NSFC (China); MINCIENCIAS (Colombia); MSES and CSF (Croatia); RIF (Cyprus); SENESCYT (Ecuador); MoER, ERC PUT and ERDF (Estonia); Academy of Finland, MEC, and HIP (Finland); CEA and CNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRI (Greece); NKFIH (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland); INFN (Italy); MSIP and NRF (Republic of Korea); MES (Latvia); LAS (Lithuania); MOE and UM (Malaysia); BUAP, CINVESTAV, CONACYT, LNS, SEP, and UASLP-FAI (Mexico); MOS (Montenegro); MBIE (New Zealand); PAEC (Pakistan); MES and NSC (Poland); FCT (Portugal); MESTD (Serbia); MCIN/AEI and PCTI (Spain); MOSTR (Sri Lanka); Swiss Funding Agencies (Switzerland); MST (Taipei); MHESI and NSTDA (Thailand); TUBITAK and TENMAK (Turkey); NASU (Ukraine); STFC (United Kingdom); DOE and NSF (USA). Individuals have received support from the Marie-Curie program and the European Research Council and Horizon 2020 Grant, contract Nos. 675440, 683211, 724704, 752730, 758316, 765710, 824093, 884104, and COST Action CA16108 (European Union); the Leventis Foundation; the Alfred P. Sloan Foundation; the Alexander von Humboldt Foundation; the Science Committee, project no. 22rl-037 (Armenia); the Belgian Federal Science Policy Office; the Fonds pour la Formation à la Recherche dans l’Industrie et dans l’Agriculture (FRIA-Belgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium); the F.R.S.-FNRS and FWO (Belgium) under the “Excellence of Science – EOS” – be.h project n. 30820817; the Beijing Municipal Science & Technology Commission, No. Z191100007219010; the Ministry of Education, Youth and Sports (MEYS) of the Czech Republic; the Shota Rustaveli National Science Foundation, grant FR-22-985 (Georgia); the Deutsche Forschungsgemeinschaft (DFG), under Germany’s Excellence Strategy – EXC 2121 “Quantum Universe” – 390833306, and under project number 400140256 - GRK2497, RTG2044, INST 39/963-1 FUGG (bwForCluster NEMO), and 396021762 - TRR 257, and the state of Baden-Württemberg through bwHPC (Germany); the Hellenic Foundation for Research and Innovation (HFRI), Project Number 2288 (Greece); the Hungarian Academy of Sciences, the New National Excellence Program - ÚNKP, the NKFIH research grants K 124845, K 124850, K 128713, K 128786, K 129058, K 131991, K 133046, K 138136, K 143460, K 143477, 2020-2.2.1-ED-2021-00181, and TKP2021-NKTA-64 (Hungary); the Council of Science and Industrial Research, India; the Latvian Council of Science; the Ministry of Education and Science, project no. 2022/WK/14, and the National Science Center, contracts Opus 2021/41/B/ST2/01369 and 2021/43/B/ST2/01552 (Poland); the Fundação para a Ciência e a Tecnologia, grant CEECIND/01334/2018 (Portugal); the National Priorities Research Program by Qatar National Research Fund; MCIN/AEI/10.13039/501100011033, ERDF “a way of making Europe”, and the Programa Estatal de Fomento de la Investigación Científica y Técnica de Excelencia María de Maeztu, grant MDM-2017-0765 and Programa Severo Ochoa del Principado de Asturias (Spain); the Chulalongkorn Academic into Its 2nd Century Project Advancement Project, and the National Science, Research and Innovation Fund via the Program Management Unit for Human Resources & Institutional Development, Research and Innovation, grant B05F650021 (Thailand); Isaac Newton Trust, Leverhulme Trust, and STFC grants ST/L002760/1, ST/K004883/1, and ST/T000694/1 (United Kingdom); the Kavli Foundation; the Nvidia Corporation; the SuperMicro Corporation; the Welch Foundation, contract C-1845; and the Weston Havens Foundation (USA).

Data Availability

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: Release and preservation of data used by the CMS Collaboration as the basis for publications is guided by the CMS policy as stated in https://cms-docdb.cern.ch/cgi-bin/PublicDocDB/RetrieveFile?docid=6032 &filename=CMSDataPolicyV1.2.pdf &version=2. CMS data preservation, re-use and open access policy].

Declarations

Conflict of interest

The authors declare that they have no conflict of interest.
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